Larry Davis borrows $75,000 at 11 percent interest toward the purchase of a home. His mortgage...

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Larry Davis borrows $75,000 at 11 percent interest toward the purchase of a home. His mortgage is for 25 years. Use Appendix

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Answer 1

Answer #1

Given information:

Borrowed amount (Principal P) = $75,000

Interest rate = 11% per annum, monthly interest rate (R) = 11/12 = 0.9167 %

Total number of years (N) = 25

Part a)

How much will the annual payment be?

We will first calculate the Equated Monthly Installment (EMI) of the mortgage, i.e. the amount that the lender will pay every month. EMI is given by the formula:

EMI = [P*R*(1+R)^N] / [ (1+R)^(N-1)] = [75,000 * 0.9167 * (1+0.9167)²⁵] / [(1+0.9167)^(25-1)] = 693.8021

Annual payment = 12 * EMI = 12 * 693.8021 = 8,325.6250

Part b:

We know Larry's annual payment.

Calculate the total payment that Larry will make to the bank. Since Larry will make this annual payment each year for 25 years, the total payment made will be 25 * 8325.625 = $208,140.625

Out of 298,140.625, the loan amount repaid is $75,000. Hence the balance amount is the interest payment which is

$208,140.625 - $75,000 = $133,140.625

Answer: Total interest payment made through the life of the loan = $133,140.625

Part c

To calculate the amount Larry is willing to pay to get out of 11% loan and get into 9 % loan, we will need to find the amount of interest saved due to switching.

For this, we will first calculate the total payment that Larry will make for 25 years with a 9% loan. Use the EMI formula again.

EMI with 9% interest =

Monthly interest rate R = 9/12 = 0.75%

EMI = [P*R*(1+R)^N] / [ (1+R)^(N-1)] = [75,000 * 0.75* (1+0.75)²⁵] / [(1+0.75)^(25-1)] = 566.7188

Annual payment = 12 * 566.7188 = 6,800.6250

Amount of money saved if Larry switches = Total payment made with 11% loan - Total payment made with 9% loan

= 25 * Annual payment with 11% loan - 25 * Annual payment with 9% loan

= 8,325.625 * 25 - 6800.6250 * 25 = $38,125

Total amount saved = $38,125

Hence Larry will be willing to pay a maximum of $38,125 to switch from 11% to a 9% mortgage.

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