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# Example 4 - Adjustable Interest Rates

This example applies to our online demo Time Value of Money Calculator. The C-Value! program for Windows works in a similar way and has a few more features. Note, our online demo TVM calculator is limited to calculations using interest rates between 2.0% and 8.9%

Conventional loan or mortgage with an interest rate change. (Adjustable Rate Mortgage or "ARM")

For greater detail about how values are entered into the TVM calculator, please see Example 1 - conventional mortgage or loan.

To create a loan schedule with an adjustable interest rate, follow these steps.

1. Click the [New] button to clear any previous entries.
2. Set "Rounding" to "Ignore" by clicking on the "Rounding" button.
1. Set compounding to "Daily".
2. Enter 8.5% for the "Nominal Annual Rate".
3. Create a "Loan" event in row one of the cash flow input area.
1. Set the "Date" to June 25, 2004 (mm/dd/yyyy)
2. Set the "Amount" to 250,000.00
3. Set the "# Periods" to 1.
4. Note: Since the number of periods is 1, you will not be able to set a frequency.
1. Move to the second row of the cash flow input area. Select "Payment" for the "Event" type. For this example, we will assume we want to create a schedule for a 15-year mortgage (180 monthly payments), which has a provision that the nominal annual interest rate can be adjusted every 5 years.
1. Set the "Date" to July 25, 2004
2. Set the "Amount" to "Unknown" by typing "U".
3. Set the "# Periods" to 180. This tells the calculator to calculate the loan as if the interest rate was not going to change. The resulting payment will be based on an 8.5% interest rate and the assumption that the rate will not change over the 15-year term of the mortgage.
4. Use the [Tab] key to tab to Frequency. Select "Monthly".
5. The "End Date" will automatically be calculated (06/25/2019). (180 monthly periods is 15 years.)

Your calculator should now look like this:

1. Calculate the unknown. The result is \$2,484.40
1. To prepare for the rate change, change the "# Periods" of payments from 180 to 60 in the second row of the Cash Flow Data. This sets the calculator so that 5 years of payments are made at the initial interest rate of 8.5%. (Reminder: If you don't have "Rounding" set to ignore, you won't be able to follow along.)
2. Move to the third row of the cash flow input area. Select "Rate Change" for the "Event" type. The "Rate Change" dialog will pop-up. The "Rate Change Date" should be set to "06/25/2009" if it isn't already.
1. Enter "6.75" for the new nominal annual interest rate.
2. Leave compounding set to "Daily". Click [OK] to close.
1. Move to the fourth row of the cash flow input area. Select "Payment" for the "Event" type.
1. Set the "Date" to July 25, 2009.
2. Set the "Amount" to "Unknown".
3. Set the "# Periods" to 120. We set this to 120 because after the 60 payments there are 120 remaining scheduled payments.
1. Calculate the unknown. The result is \$2,300.94. The payment has decrease due to the interest rate reduction.
1. To prepare for the next rate change, change the "# Periods" of payment from 120 to 60.
2. Move to the fifth row. Select "Rate Change" for the "Event" type. The "Rate Change" dialog window will open.
1. Set the date to 07/25/2014. (You can also set/reset it on the main window.)
2. Enter "8.625" for the new nominal annual interest rate.
3. Leave compounding set to "Daily". Click [OK] to close.
1. Click on the sixth row of the cash flow input area. Select "Payment" for the "Event" type.
1. Set the "Date" to July 25, 2014.
2. Set the "Amount" to "Unknown".
3. Set the "# Periods" to 60 because after the previous 120 payments there are 60 remaining scheduled payments.
1. Calculate the unknown. The result is \$2,403.75. The payment has increased due to the increase in the interest rate.
1. If you want to see a detailed amortization schedule showing the monthly payment allocated between principal and interest, click on the "Schedule" tab above the input area. Click on the [Print Preview] button (after selecting the "Schedule" tab) for an even more detailed schedule.

Below shows the "Print Preview" screen showing one of the interests rate changes.

Note that the balance after the final payment is made may not be equal to 0.00. Arriving at a 0.00 balance ultimately depends upon how the rounding options are set. Once the unknowns are calculated, you may opening the "Rounding Options" window again and set rounding to "Last Payment". After you close the window, click on [Calc] and the schedule will show a "0.00" balance.

Please Notice: Each unknown amount in the above example was calculated prior to inserting the next interest rate change. Strictly speaking, doing this would not be necessary. C-Value! will calculate multiply unknowns. However, if you calculate all unknowns at once, C-Value! will calculate the one payment amount that, when amortized, will result in a final balance being as close to 0.00 as possible. This is usually not what users want. Therefore, like a bank, the payment amount will be recalculated after each rate change event.

Summary: For adjustable rate loans, the principal to follow is calculate the payment amount for the number of ALL unknown remaining payments. After the unknown payment amount has been calculated, set the "# Periods" column to the number of payments that are to be made at the particular interest rate. Move to the next row and create a new rate change event. Then move to the next row and enter a new payment event with the amount unknown and the number of payments set to the total number of scheduled remaining payments. Again, calculate the unknown. Repeat until all payment events have been created. And after all payments have been calculated, reset the rounding option as desired.

Naturally, you can set the interest rate change date to any date desired. A rate change date does not have to fall on a payment due date.

Back to the online Time Value of Money Calculator.

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