Which of 9 Loan Calculation Options Will Save You the Most Interest?

Have you been looking `for an amortization schedule to handle a loan feature that other web calculators can't accommodate?

Or are you looking for an amortization calculator which is easy to use yet provides you with tons of details including the ability to set the original loan date followed independently by the payment start date?

Or are you looking for an amortization calculator that can create professionally printed schedules from any device?

If so, then this is the calculator for you. Scroll down the page, and below the calculator, you'll find all the options and features explained.

If, on the other hand, what you want is a quick schedule, then here is all you need to do...

- Leave all inputs and setting set to their defaults
- Enter the "Loan Amount"
- Enter expected "Number of Payments"
- Enter the "Annual Interest Rate"
- Set "Payment Amount" to "0" (the unknown)
- Click either "Calc" or "Print Preview" for your schedule

That's it! That's all you need to do to create a standard loan schedule.

But what if the terms of your loan do not conform to this calculator's default settings? Or what if you want to know what amortization method will save you the most in interest charges?

Then keep reading. All the options, as well as the **nine types of amortization schedules this calculator can create**, are explained below...»

- Calculate tax benefits
- Appreciated value
- User can set dates
- Extra payments

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*adjustable rate loan or mortgage (ARM)*? Need to enter *regular or irregular extra payments*? Need to *amortize a construction loan*? Then use this financial calculator. Users can enter multiple loan advances and adjust payment amounts and interest rates on any date.

According to Wikipedia "Amortization refers to the process of paying off a debt (often from a loan or mortgage) over time through regular payments. A portion of each payment is for interest while the remaining amount is applied towards the principal balance."

Further, "an amortization schedule is a table detailing each periodic payment on an amortizing loan (typically a mortgage), as generated by an amortization calculator."

(To be technical here, I take issue with the use of the word "regular" as used in the definition. I prefer "periodic" or "recurring" instead. Perhaps I should edit the entry?)

That's what amortization is, but the definition does not address, naturally, the different methods used for calculating an amortization schedule.

This calculator does!

It supports the following nine amortization types.

- Normal Amortization
- Rule-of-78s Payment Table
- Interest Only Payment Schedules
- No Interest Loan Schedules
- Fixed Principal Amortization
- Canadian Loan Schedule
- Amortization with Points & Annual Percentage Rate (APR)
- Loan Schedule with Final Balloon Payment
- Negative Amortization

You'll find each method discussed below.

But, before we discuss how to create the various loan tables, I need to point out some essential options impacting the initial period's interest calculations.

Important Note About Dates: This calculator supports variable length first periods. That is, the calculator calculates the exact amount of interest due even when the initial period is shorter or longer than the other scheduled periods. **Supporting odd length first periods results in more accurate calculations, but you'll see interest charges that do not match other calculators.** If you want to match other calculators, then set the "Loan Date" and "1st Payment Date" so that they equal one full period as selected in "Payment Frequency." Example: If the "Loan Date" is May 15th and the "Payment Frequency" is "Monthly," then the "1st Payment Date" should be set to June 15th, that is IF you want a conventional interest calculation.

Click on "Settings" for "Long / Short Period Options"

A long first period occurs when the period between the loan date and the first payment date is longer than the selected payment frequency. The calculator can calculate the interest due for these extra or odd days in one of four ways.

- None - free money! No interest calculated on the odd days
- With first - odd day interest paid with first payment due. Payment will be larger than the other periodic payments.
- With origination - odd day interest is due when the loan originates - commonly known as "prepaid interest"
- Amortized - a small amount of odd day interest is paid with each payment. The calculator increases all payments to be equal.

A short first period occurs when the period between the loan date and the first payment date is shorter than the selected payment frequency. The calculator can calculate the interest due for the short period in one of three ways.

- No payment reduction - the calculator calculates what is considered to be a "normal" normal payment amount and uses it for the first payment. The last loan payment is reduced to compensate for the short period
- Reduce first - the first payment is reduced to compensate for the short period
- Reduce all - all payments are reduced to compensate for the short period.

Here's a more formal definition of odd days interest from the Financial Dictionary.

One more comment about dates.

By default, the schedule's totals are calculated as of December 31.

But some taxpayers pay taxes based on a different year-end. This calculator supports annual and cumulative totals as of any month end.

Click the "Settings" button and select "Year End Month."

If in doubt, use this setting when amortizing a loan. In the US at least, nearly all loans use the "normal" method.

These are the characteristics of a normal loan or mortgage:

- They have "level payments" i.e., the scheduled periodic payment amount does not change. (With the possible allowance, as discussed above, for odd day interest.)
- The interest amount paid declines each period as the loan balance is being paid down.
- Thus, the principal amount paid each period increases to keep the payment amount level.
- There may be a slight adjustment ("rounding") of the final payment so that the loan is brought to a 0 balance.

The next method, consumers will want to avoid.

The Rule-of-78s method front loads the interest due. That is, the debtor pays more interest early in the payment schedule and less interest later when compared to a "normal" loan.

Both the periodic payment amount and the total loan interest due are the same for both the Rule-of-78s and the "normal" methods. The only difference is how the interest gets allocated each period.

The blog post here thoroughly explains the Rule-of-78s amortization and why, as a consumer, you may want to avoid such loans.

For the lowest periodic payment, get a loan using the next payback method. There's only one catch...

Some loans require the borrower to pay only the interest due each period. Such loans are known as "interest only loans"

These are the characteristics of an interest only loan or mortgage:

- The periodic payment amount generally does not change.
- The interest amount paid each period is the same because no principal is paid, the loan balance does not change.
- The entire principal balance plus the last period's interest is due with the last payment.

If you think that interest only loans are not very common, then think again.

Many bonds sold to investors are interest only loans. The bond's buyers are lending the issuer money. The bonds pay the buyer a periodic coupon payment which is the interest on the debt. And as reported by Zacks the size of the bond debt in the US at "the end of 2017 was more than $40.7 trillion"

That's a lot of debt financed with interest only payments!

If you represent a bond issuer, you can prepare a bond coupon payment schedule with this amortization calculator. The "loan date" is the bond's issuance date and the "first payment date" is the date of the first coupon payment. Make sure to select the "Interest Only" amortization method.

Yes, it happens! I added this amortization method to the Windows version of this calculator 20 or more years ago. Someone called me (remember phone calls?) and said he and his wife were lending money to their son and they wanted to create a payment schedule that they could agree to, the catch was, there would be no interest charged.

This amortization schedule continues to support an interest-free loan.

You may ask, "Why not just enter a "0" interest rate?"

The answer is simple. If a user enters a "0" for any input, then the calculator interprets that as the unknown value. So if a user enters a "0" for the interest rate, the calculator will attempt to calculate the rate.

To get around this, select the "No Interest" option for an amortization method.

The following amortization method will save you interest charges if you can afford it.

Before computers and calculators, that is, before it was easy to calculate a level payment amount, lenders frequently had lenders payoff loans using the fixed principal amortization method.

Why?

Determining the payment amount requires only simple arithmetic. To calculate the payment due, first, divide the principal loan amount by the number of payments in the term and then add the periodic interest.

These are the characteristics of a fixed principal loan or mortgage:

- Payment amount start higher than a "normal" loan.
- The loans feature a declining payment amount. As the borrower pays down the principal balance, the interest due each period is reduced and therefore the payment decreases over time.
- The principal amount paid each period is fixed. The principal paid on a $1,200 loan with a term of one year will always be $100.
**The borrower pays less total interest**- There may be a slight adjustment ("rounding") of the final payment so that the loan is brought to a 0 balance.

The Canadian amortization method is the same as the "normal amortization method" except for one detail. When the user selects the Canadian method, the calculator automatically sets the payment frequency to monthly and the compounding frequency to semiannual.

A conventional loan typically uses the same frequency for both payments and compounding.

The Canadian method, because it uses less frequent interest compounding, results in a slightly lower scheduled payment amount because the interest due is somewhat less each period when compared to the interest charges owed under monthly compounding.

For more details, here's a A Guide to Mortgage Interest Calculations in Canada.

Occasionally, there are times when the terms of a loan call for a payment to be calculated on a 30-year payback but the loan will come due after five years of payments (for example).

Because the payment calculation uses a 30-year term, the balance of the loan will still be substantial relative to the starting balance when the term is up in five years, and the balance is due.

Creating an amortization schedule showing the balloon payment amount is simple with this calculator.

- First...
- Enter the loan amount
- Enter the interest rate
- Enter the number of payments which will be used to calculate the periodic payment due - in this case 30-years or 360 monthly payments.
- Enter "0" for the payment amount and click on "Calc"

- Then....
- Change the number of payments to the actual term of the loan - per this example that's 5 years or 60 payments
- Click on "Print Preview" to see your amortization schedule with a balloon payment.

balloon payment calculator. It creates a schedule too.

Need to calculate a regular periodic payment amount that results in a specific final balloon payment? Then see this site'sSome loans require the borrower to pay an upfront charge called "points."

Why would a borrower be willing to pay an extra charge?

When the borrower pays points, the lender reduces the interest rate. Points are in essence prepaid interest (and the IRS treats them that way). One point is one percent of the loan amount. Thus, one point on a $300,000 is equal to $3,000.

The user has two choices for how to create an amortization schedule with points. Click on "Settings" and select "Points, Charges & APR Options."

If "Include dollar value of points in interest charges" is checked then the calculator calculates the dollar cost of the points, and the payment schedule shows them paid at the loan origination. The calculator also adds the cost of points to the total interest charges.

If the user didn't check this option, then the dollar value gets reported in the header only, and the amount does not get added to the total interest.

See Moving.com "What Are Mortgage Loan Points?" for more details.

Points impact the loan's annual percentage rate. If you want to check the APR (and if you are the borrower, you should), you can include a Truth-in-Lending Act compliant calculation in the schedule's footer. Just check the option "Include Regulation "Z" APR Disclosure calculation at the end of the schedule?". For an accurate APR, don't forget to include any fees in "Other charges & fees (for APR calculation)?" input.

APR Calculator and Disclosure Statement. This calculator calculates APR and creates a printable disclosure statement.

If you have any questions about APR calculations and what fees to include or exclude, see this site'sUsers frequently tell me they use this calculator to "check their lender's payment amount."

That's fine, of course. But all borrowers should also understand, there is no such thing as a "correct payment amount." The only payment amount of concern is the amount agreed to between the lender and borrower. All things being equal if the lender says the payment is $315 a month and the borrower expects it to be $311 a month, it doesn't matter - as long as they both agree on the initial period's calculated interest amount. If the parties agree on the interest calculation, then paying a slightly higher amount will pay the loan off marginally faster or result in a smaller final payment, and the total collected as interest will be slightly less.

So what does this have to do with negative amortization?

Simple, if the lender and borrower agree on an amount that is not large enough to pay the interest due it results in negative amortization.

This amortization calculator gives the user the ability to set any payment amount. Rather than enter a "0" for the payment, enter the agreed upon payment amount.

When the payment amount is less than the periodic interest due, the loan balance will increase each period because the interest not covered by the payment must get added to the balance.

There is nothing wrong with a negatively amortizing loan per say. However, the borrower will have to be prepared to pay a single, large payment at the end of the term.

If you are the borrower, be sure to check the last payment row of the schedule for the final payment amount, which includes the accrued interest, to see if you can handle it.

Note the negative principal amounts in the below figure.

From time-to-time, I get requests from users for the ability to export an amortization schedule to Excel. This calculator won't do that. However, users can select the data and copy/paste to Excel.

You can copy/paste from either the main window or from the print preview window. If you copy from the main window, then formatting will remain intact. If you copy from the print preview window, then only the values will be copied. Depending on the browser you are using, you may have to use Excel's **Paste Special** feature and select "Text" for copy/paste to work.

If you want to copy from the main window, I think the easiest way to do that is to scroll to the end of the schedule and select the last row and then scroll upwards to select the entire table.

C-Value! for Windows program is even more flexible than this calculator and it will export directly to Excel.

MyIf you want to share this calculator's schedule with someone or save it in a digital format for later reference, you can print the results to a PDF file.

If you are using Google's Chrome browser, printing to PDF is a standard feature. Click on Chrome's menu (the 3 verticle dots) and select "Print..." Click on the "Change..." button and select "Save as PDF."

If you are not using a browser that supports printing to a PDF, no problem. You can install a PDF print driver. It pretty easy to do this. And there are many free ones from which to pick. In the past, I used PrimoPDF.

By the way, one advantage of installing a PDF print driver, even if you use Chrome, is you'll then be able to create PDF files from any application you use, not just your browser.

**Make sure, when saving to PDF that you use the "Print" button on the "Print Preview..." window.**

C-Value! for Windows program is what you need. It is even more flexible than this calculator, and you can save your work to a file for later recall.

Do you want to be able to save your inputs to a file so you can later edit them or reprint the schedule? Then theActually, there's not a lot to say about printing...

Users should know that printing is expected to work from any device. It's pretty cool to print a well-formatted schedule from a smartphone that is connected wirelessly to a modern printer. (I've personally tested this using an iPhone 5 and iPhone X printing to an HP LaserJet Pro 400.)

Make sure you are printing from the "Print Preview..." window where there are two print buttons available.

If you have any problems, please let me know what browser and version you are using. I can test various browsers, but unfortunately, I can't check too many printers (unless you are prepared to donate one to the cause!).

**free online loan payoff calculator**. For a step-by-step example see the payoff calculation tutorial.

Or what would you lke to know?

While this page covers a lot of material on amortization schedules, it can't cover everything.

Let me know in the comments below what I missed. Or feel free to ask your questions and I'll answer them (to the best of my ability).

Naturally, you can also tell me what I got right. Tell me what feature is particularly useful to you that you did not find in other online calculators.

MS Excel® is a registered trademark of the Microsoft Corporation.

Every loan has four primary attributes or variables. (1) The loan amount, (2) the number of payments, (3) the annual interest rate and (4) the payment amount.

Enter any 3 values and zero ('0') for the unknown value. Click the "Calc" button to solve for the unknown and create a schedule.

Note: you can enter a non-zero value for all 4 variables. In that case, your inputs will be used to create the amortization schedule.

The "Loan Date" is the date the monies are advanced. It is also called the "origination date".

The "First Payment Date" is the date the first payment is due. It may be the same date as the "Loan Date" but not usually. When they are the same, this is known as "Payment-in-Advance". Leases are typically paid-in advance.

"Payment Frequency" determines how often payments are due. Monthly is the most common in the USA.

"Compounding" impacts how interest is calculated. In most cases "Compounding" should equal the "Payment Frequency".

"Points" are charged on some loans by the lender. Points are expressed as a percentage of the loan amount. A 300,000.00 loan with 2 points results in an extra fee due the lender of 6,000.00. Points are common for mortgages in the US only. Normally, you will want to leave this input set to 0.0%.

To print any loan schedule, click on "Print Preview" and then "Print this schedule". "Print Preview" will also function as a "Calc" button.

- mortgage calculator — calculate future home value and compare to total mortgage cost
- loan calculator — supports extra payments and dates in a more mobile friendly design
- auto loan calculator — calculate total cost of ownership
- biweekly calculator — in one schedule, compare a biweekly loan to a normal loan
- financial calculator — create schedules with missed payments and changing rates

Hello Karl,

I followed your lead and focused exclusively on the interest calculation.

Again using the following data: Loan = $32,500; APR = 7.5%; Payments # = 8; Loan Date = 07/01/2018; First Payment Due: 08/01/2018; Payment Frequency: Monthly; Compounding: Weekly; Points: 0%; Amortization Method: Normal; Days per year: 360.

Using these variables your calculator, interest on the first installment amounts to $208.34

In this instance I used the standard textbook formula for compounding interest—> S = P*(1+R/N)^(N*T)-1

S = value of principal and interest; P = original principal amount; R = annual percentage rate; N = number of years; T = number of compounding periods in 1 basis year. Data used is P = $32,500; R = 7.5%, N = 52 (weeks in year)

I assume that for a term of 1 month (from 07/01/18 to 08/01/18), T = 0.083333333 or 1/12th of one year.

Using these variables S = $32,703.61. After subtracting the principal ($32,500), the interest for 1 month will equal $203.61

So I am stuck with a difference which I cannot explain from basic textbook mathematics.

Hoping to hear from you.

Kind regards,

Mark

Hi Mark, First, I guess I should have pointed it out in the prior reply that I do not provide support for the equations. My support is limited to two types of questions:

But that said, your assumption about T is wrong if you want weekly compounding. That’s monthly compounding.

Thanks Karl

I have a loan schedule from your website for a second mortgage with a 30-year payout and a 5-year balloon. The original loan date was 06/05/2014 and the interest rate was 4.0000%, with monthly payments of $1,069.41. I need to amend the interest rate to 5.0000% as of 07/05/2018, with the end date remaining the same. Can you tell me how to do that? Is that possible? Help! Thanks.

Yes, this is possible, but not with this calculator.

You’ll need to use the Ultimate Financial Calculator on this site.

It creates an amortization schedule that also allows the user to change the interest rate on any date. You can also record payments on the dates they are made. With this flexibility comes a bit more complexity, however. If you try this calculator, scroll down the page to the 25 tutorials. Read #1 to get an overview. Then in the list there’s a tutorial that deals with rate changes and two about balloon payments.

Naturally, if you have a question, just ask.

Thanks Karl for creating such a beautiful site. Its really helpful.

I am trying to get the loan repayment schedule for below data :

Loan Amount?: $20,000.00 Payments? (#): 10

Annual Interest Rate?: 2.5% Payment Amount?: $0.00

Loan Date?: 06/26/2018 First Payment Due?: 05/05/2019

Payment Frequency?: Annually Compounding?: Daily

Points (%)?: 0.0% Amortization Method?: Normal

The loan repayment schedule given by above calculator is :

Date Payment

05/05/2019 2,219.37

05/05/2020 2,293.33

05/05/2021 2,293.33 (same payment til 2028)

Here i have a question can we get the equal payment amount spread across for 10 installments? If possible could you please share the formula used to calculate the Payment installments for above scenario?

You’re welcome. I appreciate the compliment.

This particular loan is what we call a loan with an "initial short period." That is, the time between the loan date and the first payment is shorter in duration than the selected payment frequency. As you’ve discovered, this calculator defaults to reducing the first payment to compensate.

If you want all payment amounts to be the same (except for the last payment which is subject to rounding), you have 2 choices: 1) Rather than set the payment amount to 0 to have the calculator calculate it, set the payment amount to what you want i.e. $2,293.33. All payments, including the first will be this amount. The last payment will show a great deal of rounding since this "extra" (diff between $2,219 and $2,293 is applied to principal). 2) You can also use this calculator. Under the "Settings" options there will be interest options and there you’ll find options for setting how to handle short periods. If you try this calculator, scroll down the page and check out the tutorials.

Thanks Karl for your reply.

I used the option 2 for loan repayment (10 equal repayment with annual frequency where the first repayment is “initial short period”). I used the interest options setting for short periods as “Reduce All”. This is working exactly as per my requirements. Is it possible for you to share the formula used for this type of calculation. I need to use the similar formula for my calculation on one of my assignments.

You’re welcome. Glad the option give you what you needed.

Vishal, I have to limit my support to 2 types of questions. Either the question has to relate to how to use a calculator or what calculator to use to solve a problem.

I’ll add for your case, there is no formula or equation per say that produces the results the calculator gave you. Rather an "algorithm" is used to solve this type of problem. It takes several thousand lines are programming code to get to the answer. If I supported the "how", I would never have time left to create more calculators.

Thanks Karl

My first payment was 3/15/2018. My loan date was 1/24/2018.

The amortization schedule makes a payment on the 1/24/2018 date, this payment should be 0.0.

Please explain how to prevent a payment on 1/24/2018 since all subsequent monthly payments are incorrect.

With pleasure. What you have is a long initial period, assuming your loan has monthly payments. That payment on 1/24/2018 is for the initial "odd days interest, " that is the interest from 01/24/18 to 02/15/18.

This calculator has options for setting when the odd day interest is paid.

Click on the "Settings" button and select "Long/Short Period Options."

Scroll down the page from the calculator and see the subheading "About Dates, First Period Interest & Year-End Totals" where you can read more about these options.

Hi Karl,

I am looking for a program that will recalculate when extra payments are made. ie Amortization calls for a payment of $500.00 per month. payor pays $ 550 one month then $600 the next and then $500. is their a program that will do this?

Yes, there are a couple of options for extra payments. But if the extra payment amount is going to vary month to month, then use this calculator.

Once on that page, scroll down and check out tutorial #9, random extra principal payments. (Check out tutorial #1 too to get started.)

Hi:

I need to do a loan with set payments for the first two years, then a balloon payment for the 25th payment. I need to do the same thing, but then have the payment amount change at the end of the 24 months, with no balloon payment. I need to show my customer both options. How can I do this? Please help

As you many have discovered, this calculator will handle the first calculation, but not the second. I will not allow the payment amount to change.

No problem though, just switch calculators. Please see the Ultimate Financial Calculator. It will allow you to change the payment amount (or interest rate) on any date. If you go to the page, scroll down and see the tutorials. Read #1 for an overview, and then there are two dealing specifically with balloon payments.

Once on that page, if you have any questions, just ask.

What about payments made in advance mode (BOM) versus arrears mode EOM)? how are the calculations and tables different? do you have a model that does this based on inputs?

This calculator supports "payments-in-advance". For lurkers, payment in advance simply means the payment at the beginning of a period, before any interest is due.

To setup such a scenario with this calculator, set the loan date and 1st payment date to be equal. When you run a schedule, notice there is no interest for the first payment.

Now, if you want payment in advance, and the loan date does not equal the first payment date, the use the interest options under "settings" and set the long/short period interest option to reduce first payment. With payment in advance and if the loan date and first payment date are not equal, the duration between the two must be less than the length of the regular period, otherwise, the payment is late and all bets are off.

If this isn’t clear, please ask for clarification.

I don’t understand. If the payment is due at lease commencement of a lease, and the payment mode is BOM, why would there be no interest earned in month 1

First, I wasn’t aware we were discussing a lease. I was speaking about a loan.

But to answer your question, with a loan, at the time a payment is made, the interest due is calculated and added to the balance. The payment is then deducted from the balacn. If the first payment is made on the day the loan is advanced (BOM), the money will have been borrowed for 0 days and therefore calculated interest equals 0. Interest will not have accrued until the 2nd payment is due.

Now some leases may work differently than a loan. They may have precomputed interest added to the balance. That is, the interest is charged to the first payment even though the interest has not been earned (again, since no days have passed.) If so, then this calculator will not work for those cases.

(As an aside, following a BOM payment method is an easy way for the consumer to save money. All the consumer has to do is to make the 1st payment when the loan is issued. This calculator shows that clearly. Compare the total loan interest between the two methods without changing the payment amount.)

How do I calculate the following:

175000 loan at 3% annual interest. Date of loan is 10/24 with first payment due 12/15 and remaining payments on 9/15 and 12/15 of each of next three years.

Please help, I am struggling with it and which calculator to use.

Thank you.

You’ll need to use the Ultimate Financial Calculator for what you want to do. This amortization schedule would work for any loan with a regular payment schedule. Your loan doesn’t have a regular schedule.

Once on the above page, scroll down to the list of tutorials and check out tutorial #1 for an overview. Once you do that, and if you have any questions, just ask. The calculator will definitely do what you need.

Thank you Karl, worked great.

If this were a business loan, would you use 360 day or 365 day? What is most common or the proper one to use?

Thank you.

You’re welcome, Sam. Glad to hear that it worked for you.

As to the days per year question, there just isn’t a right or wrong. 360 results in higher interest and therefore is more beneficial to the lender. And, of course, if you are the borrower, you would want 365.