The table shows the specifications of an adjustable rate mortgage​ (ARM). Assume no caps apply. Find​ a) the initial monthly​ payment; b) the monthly payment for the second​ adjustment; and​ c) the change in monthly payment at the first adjustment.

Question

​*The principal balance at the time of the first rate adjustment.
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Part 1
Beginning Balance
​$85,000
Term
20 years
Initial index rate
​5.3%
Margin
​2.7%
Adjustment period
1 year
Adjusted index rate
​6.8%
​*Adjusted balance
$83,203.43​

What is the initial monthly​ payment?
What is the monthly payment for the second adjustment​ period?

Answer 1

To find the initial monthly payment, we need to use the formula:

Initial Monthly Payment = (Adjusted Balance * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate) ^ (-number of payments))

1. Calculate the Monthly Interest Rate:
Monthly Interest Rate = (Initial Index Rate + Margin) / 12
= (5.3% + 2.7%) / 12
= 0.88% / 12
= 0.00733

2. Calculate the Number of Payments:
Number of Payments = Term * 12
= 20 * 12
= 240

3. Insert the values into the formula:
Initial Monthly Payment = (83,203.43 * 0.00733) / (1 - (1 + 0.00733) ^ (-240))

Using a financial calculator or software, the initial monthly payment is approximately $590.57.

To find the monthly payment for the second adjustment period, we need to use the adjusted index rate.

1. Calculate the Monthly Interest Rate for the second adjustment period:
Monthly Interest Rate (2nd Adjustment Period) = Adjusted Index Rate / 12
= 6.8% / 12
= 0.5667%

2. Insert the values into the formula used in the previous step:
Monthly Payment (2nd Adjustment Period) = (83,203.43 * 0.005667) / (1 - (1 + 0.005667) ^ (-240))

Using a financial calculator or software, the monthly payment for the second adjustment period would be approximately $584.35.

To find the change in monthly payment at the first adjustment, we subtract the initial monthly payment from the monthly payment for the second adjustment.

Change in Monthly Payment = Monthly Payment (2nd Adjustment Period) - Initial Monthly Payment

Change in Monthly Payment = $584.35 - $590.57

The change in monthly payment at the first adjustment would be approximately -$6.22.