A family has a $93,411, 20-year mortgage at 5.4% compounded monthly. Find the monthly payment. Also find the unpaid balance after 5 years and after 10 years The monthly payment is SO. (Round to two decimal places.)

payment: $637.30 5-year balance: $78,505.48 10-year balance: $58,991.59

Step-by-step explanation:

1. The relevant formula for computing the monthly payment A from principal P and interest rate r for loan of t years is ...

A = P (r/12) / (1 - (1 + r/12) ^ (-12t))

Filling in the numbers and doing the arithmetic, we get ...

A = $93,411 (0.054/12) / (1 - (1 + 0.054.12) ^ - (12·20)) ≈ $637.30

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2. The relevant formula for computing the remaining balance after n payments of amount p on principal P at interest rate r is ...

A = P (1 + r/12) ^n - p ((1 + r/12) ^n - 1) / (r/12)

Filling in the given values and doing the arithmetic, we get ...

A = $93,411 (1.0045^60) - 637.30 (1.0045^60 - 1) / (0.0045) ≈ $78,505.48

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3. The same formula with n=120 gives ...

A = $93,411 (1.0045^120) - 637.30 (1.0045^120 - 1) / (0.0045) ≈ $58,991.59