Question

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.)

Answer 1

Answer:

• 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