5. Kenny purchases a new home with a $300,000 mortgage loan at 5% annual effecti

Question

5. Kenny purchases a new home with a $300,000 mortgage loan at 5% annual effective rate of interest. He makes payments monthly for 30 years with the first payment made one month from the loan origination.

a. What is the effective monthly interest rate?

b. What is the monthly payment?

c. What is the balance of the loan after the 99th payment?

d. Suppose that starting with the 100th payment, Kenny adds $500 to each payment in order to repay the mortgage earlier. How many payments are required with the new increased payment?

e. What would be the remaining balance one month before the final payment is due? f. What would be the amount of last payment?

Explanation / Answer

Answer a The effective monthly interest rate = 5%/12 = 0.4167% Answer b Calculation of monthly payment using present value of annuity formula PV of annuity = P*{[(1-(1+r)^-n] / r} PV of annuity = loan amount = $300000 P = monthly payment = ? r = rate of interest per month = 0.4167% n = no.of monthly payments = 30 years * 12 = 360 300000 = P*{[(1-(1+0.004167)^-360] / 0.004167} 300000 = P*{0.776173 / 0.004167} 300000 = P*186.27 P = 1610.59 Monthly payment = $1610.59 Answer c Calculation of the balance of the loan after the 99th payment using present value of annuity formula PV of annuity = P*{[(1-(1+r)^-n] / r} PV of annuity = loan balance after 99th payment = ? P = monthly payment = 1610.59 r = rate of interest per month = 0.4167% n = no.of remaining monthly payments = 360 - 99 = 261 PV of annuity = 1610.59*{[(1-(1+0.004167)^-261] / 0.004167} PV of annuity = 1610.59*158.92 PV of annuity = 255960.52 The balance of the loan after the 99th payment = $2,55,960.52 Answer d Calculation of the no.of monthly payments required using present value of annuity formula PV of annuity = P*{[(1-(1+r)^-n] / r} PV of annuity = loan balance after 99th payment = ? P = monthly payment = 1610.59+500 = 2110.59 r = rate of interest per month = 0.4167% n = no.of monthly payments required = ? 255960.52 = 2110.59*{[(1-(1+0.004167)^-n] / 0.004167} 121.27 = [(1-(1+0.004167)^-n] / 0.004167 n = 169.26 No.of monthly payments are required with the new increased payment = 169

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