Question

Larry Davis borrows $75,000 at 11 percent interest toward the purchase of a home. His mortgage is for 25 years. Use Appendix D for an approximate answer, but caloulate your final answer using the formula and financial calculator methods. a. How much will his annual payments be? (Athough home payments are usually on a monthly basis, we shall do our analysis on an annual basis for ease of computation. We will get a reasonably accurate answer (Do not round Intermediate calculations. Round your final answer to 2 decimal places.) Annual payments b. How much interest will he pay over the ife of the loan? (Do not round intermediate calculations. Round your final answer to 2 decimal places.) Aneual payments G. How much should he be willing to pay to get out of a 11 percent mortgage and into a 9 percent mortgage with 25 years remaining on the mortgage? Assume current interesst rates are 9 percent. Carefuly consider the time value of money. Disregard taxes. (Do not round intermediate calculations. Round your final answer to 2 decimal places.) Annual payments

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.