# Time Value of Money TutorialsTVM Calculations

## How to Calculate a Loan with an Irregular Length First PeriodTutorial 13

Nearly every loan has an irregular or odd length first period. An irregular length first period happens when the debtor borrows money on one date and the payments are due on a different date. This financial tutorial discusses the various options available for the initial period's interest calculation. Your choice can impact the periodic payment amount as well as the total interest collected over the term of the loan.

Example: By convention, in the US, mortgage payments are typically paid monthly and are due on the first of the month. If a real estate transaction closes on July 15th and the first payment is not due until September 1, an odd length first period is created — specifically a "long first period". The effect of this is that more interest is due the lender. This "extra" interest due to the initial odd days (July 15 - August 1) can be collected in one of three ways as described later in this tutorial. If the transaction closes on August 15th with the first payment still due on September 1st, then we have a "short first period".

Important: We think it is important to be aware of these options. Short and long odd period interest settings impact the calculation of every loan that does not have a regular length first period. In fact, if the "Amortized" option is selected, every loan payment will be impacted. (The payment amount will be higher than what is expected because a portion of the odd day interest is paid with each payment.)

This example applies to our online Ultimate Financial Calculator. The C-Value! program for Windows works in a similar way and has a few more features including the ability to save your work.

All users should work through the first tutorial to understand basic concepts about the calculator.

To create an amortization that has an odd length first period, follow these steps:

1. Set "Schedule Type" to "Loan"
• Or click the [Clear] button to clear any previous entries.
• The top two rows of the grid will not be empty
• Delete the 2nd row by selecting it and clicking on the [Delete] button
2. Set "Rounding" to "Open balance — no adjustment" by clicking on the {Settings} {Rounding Options}
3. In the header section, make the following settings:
1. For "Calculate Method" select "Normal".
2. Set "Initial Compounding" to "Daily".
3. Enter 6.5 for the "Initial Interest Rate".
1. In row one of the cash flow input area, create a "Loan" series
1. Set the "Date" to July 15, 2016
2. Set the "Amount" to 425,000.00
3. Set the "# Periods" to 1
• Note: Since the number of periods is 1, you will not be able to set a frequency. If a frequency is set, it will be cleared when you leave the row
1. Move to the second row of the cash flow input area. Initially, the regular payment amount is unknown
1. Select "Payment" for the "Series"
2. Set the "Date" to "September 1, 2016"
3. Set the "Amount" to "Unknown"
4. Set the "# Periods" to 360
• Before the calculation, your screen will look like this:
• The Ultimate Financial Calculator has four options for how the long period interest (also call "odd days interest" is calculated. In this example, the odd day interest is the interest, which is due the lender for the period from July 15 to August 1. More below
1. Click {Settings} menu and select {Interest Options}. This opens the "Initial Period Interest Payment Options" window
• The four options for long period interest are:
• "None" Odd day interest is ignored. Fat chance!
• "With origination" Odd day interest is collected on the loan date. That is, the day the monies are advanced, July 15th in this case
• "With first" The interest is collected "with the first payment"
• "Amortized" The interest is paid evenly" which means all payments will be increased slightly
1. Select "With origination"
1. Calculate the unknown:
• The result is \$2,686.29 when the odd day interest is paid on the loan origination date (or along with the first payment)
• The result is \$2,694.53 when the odd day interest is amortized (added to each payment)
1. Check the amortization schedule by clicking the [Schedule] button:
• The \$1,304.58 payment is for the interest due from July 15th to August 1st
• There are three options for an initial short period
• Since the period is shorter than the other periods there is no odd day interest to collect
• A short initial period accrues less interest and there are 3 available options for handling short periods:
• "No payment reduction" A larger portion of the payment is applied to principal. (This saves interest charges over the term of the loan)
• "Reduce first" All other payments will be the same
• "Reduce all" Make all payments slightly less than they otherwise would have been.

There are a number of ways lenders can calculate interest for irregular initial periods. Regardless of the method a lender uses, the Ultimate Financial Calculator makes it easy to audit the result.

Back to the online Ultimate Financial Calculator.