Question

5. Suppose you borrow $300,000 for a home mortgage on January 1, 2020 with an annual interest rate of 6% per year. The balance on the mortgage is amortized over 25 years with equal monthly payments at the end of each month. (This means the unpaid balance on January 1, 2045 should be $0).

(a) What are the monthly payments?

(b) How much interest was paid during the 25 years of the mortgage?

(c) What is the unpaid balance on the mortgage on January 1, 2030?

Answer 1

Loan Amount = $300,000

a). Calculating the Monthly Payment of Loan:-

Where, P = Loan Amount = $300,000

r = Periodic Interest rate = 6%/12 = 0.5%

n= no of periods = 25 years*12 = 300

Monthly Payment = $1932.90

b). Interest Paid over 25 years of Mortgage = (Monthly Payment*no of Payments) - Loan Amount

= ($1932.90*300) - $300,000

= $279,870

c). Calculating unpaid balance on Mortgage on 1 Jan, 2030:-

Where, P = Loan Amount = $300,000

r = Periodic Interest rate = 6%/12 = 0.5%

n= no of periods = 25 years*12 = 300

m = No of periods Lapsed = 10 years*12 = 120 (From 1 Jan, 2020 to 1 Jan, 2030)

Outstanding Balance = $229,055.94

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