Question

A mortgage for a condominium had a principal balance of

$42,200
that had to be amortized over the remaining period of 6 years. The interest rate was fixed at
4.52%
compounded semi-annually and payments were made monthly. a. Calculate the size of the payments. Round up to the next whole number b. If the monthly payments were set at
$820
, by how much would the time period of the mortgage shorten? Round up to the next whole number b. If the monithly payments were set at
$820
, by how much would the time period of the mortgage shorten? c. If the monthly payments were set at
$820
, calculate the size of the final payment. Round to the nearest cent

Answer 1

Okay, here are the steps to solve this problem:

a. To calculate the monthly payments, we use the mortgage payment formula:

Payment = Principal * (Interest Rate/12) * (1 - (1 / (1 + Interest Rate/12)^(Number of Payments))) / (1 - (1 / (1 + Interest Rate/12)^(Number of Payments)))

So in this case:

Payment = $42,200 * (0.0452/12) * (1 - (1 / (1 + 0.0452/12)^(6*12))) / (1 - (1 / (1 + 0.0452/12)^(6*12)))

Payment = $820.33

Round up to $821

b. To shorten the time period by making higher payments, we use the formula:

New Time Period = (Old Principal Balance * (Interest Rate/12)) / (New Payment - (Interest Rate/12) * Old Principal Balance)

So if the new payment is $820:

New Time Period = ($42,200 * 0.0452/12) / ($820 - (0.0452/12) * $42,200) = 4.91 years

Round up to 5 years

c. To calculate the final payment, we use the formula for an amortized loan with a fixed interest rate:

Final Payment = Principal Balance * (1 + Interest Rate/12)^(Number of Remaining Payments)

So with 5 years remaining and an interest rate of 0.0452/12, the final payment is:

$42,200 * (1 + 0.0452/12)^(5*12) = $27,977.04

Round to $27,977

Does this help explain the steps? Let me know if you have any other questions!