Question

You are taking out a $100,000 mortgage loan to be repaid over 25 years in 300 monthly payments.

a. If the interest rate is 16% per year, what is the amount of the monthly payment?

b. If you can only afford to pay $1,000 per month, how large a loan could you afford to take?

c. If you can afford to pay $1,500 per month and need to borrow $100,000, how many months would it take to pay off the mortgage?

d. If you can pay $1,500 per month, need to borrow $100,000, and want a 25-year mortgage, what is the highest interest rate you can pay?

I need to show work without using a financial calculator.

Answer 1

a) Monthly Payment can be calculated using PMT function on a calculator

N = 300, I/Y = 16%/12 = 1.33%, PV = 100,000, FV = 0

=> Compute PMT = $1,358.89 should be the monthly payment

b) Loan amount can be calculated using PV function

N = 300, I/Y = 1.33%, PMT = 1000, FV = 0

=> Compute PV = $73,589.53

c) Period can be calculated using N function

PV = -1500, I/Y = 1.33%, PV = 100,000, FV = 0

=> Compute N = 165.9 or 166 months.

d) Interest rate can be calculated using I/Y function

N = 300, PV = 100,000, FV = 0, PMT = -1,500

=> Compute I/Y = 1.48% (monthly)

Annual Rate = 1.48% x 12 = 17.78% is the max interest rate.