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?

Answer 1

To calculate the initial monthly payment, we need to use the formula for an adjustable rate mortgage:

Initial Monthly Payment = (Adjusted Balance * (Adjusted Index Rate + Margin)) / (1 - (1 + Adjusted Index Rate)^(-Term))

Plugging in the given values:

Adjusted Balance = $83,203.43
Adjusted Index Rate = 6.8%
Margin = 2.7%
Term = 20 years

Initial Monthly Payment = ($83,203.43 * (6.8% + 2.7%)) / (1 - (1 + 6.8%)^(-20))

Calculating the expression:

Initial Monthly Payment = ($83,203.43 * 9.5%) / (1 - (1 + 6.8%)^(-20))

Next, we need to convert the percentages into decimal form:

Initial Monthly Payment = ($83,203.43 * 0.095) / (1 - (1 + 0.068)^(-20))

Calculating the value inside the parentheses:

Initial Monthly Payment = ($7,894.33) / (1 - (1 + 0.068)^(-20))

Next, we calculate the expression inside the second set of parentheses:

Initial Monthly Payment = ($7,894.33) / (1 - (1.068)^(-20))

Calculating the exponent:

Initial Monthly Payment = ($7,894.33) / (1 - 0.37689)

Next, we calculate the subtraction inside the parentheses:

Initial Monthly Payment = ($7,894.33) / (0.62311)

Finally, we can solve for the initial monthly payment:

Initial Monthly Payment ≈ $12,665.07

Therefore, the initial monthly payment is approximately $12,665.07.