Question

Derek planned to buy a house but could afford to pay only $9,500 at the end of every 6 months for a mortgage with an interest rate of 4.90% compounded semi-annually for 25 years. He paid $20,500 as a down payment.

a. What was the maximum amount he could afford to pay for a house?

Round to the nearest cent

b. What was his total investment through the mortgage period (not taking the time-value of money into account)?

Round to the nearest cent

c. What was the total amount of interest paid through the mortgage period?

Round to the nearest cent

Answer 1

He could pay $ 9,500 every six months

Interest rate = 4.90% compounded semi annually

Tenure = 25 years = 50 payments

Down payment = $ 20,500

Present value = 20,500(P/A,4.9%,50)

PW = 9,500 x 1 - 1.0245-50 0.0245

S PW = 9,500 x 28.64786

PW ~$ 272, 155

Maximum amount he could afford to pay for a house = $ 20,500 + 272,155

= $ 292,655

B. Total investment = 50 payments of $ 9,500 = $ 475,000

C. Total interest paid = 475000 - 272155 = $ 202,845

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