Question

The problem describes a debt to be amortized. (Round your answers to the nearest cent.) A man buys a house for $340,000. He makes a $150,000 down payment and amortizes the rest of the purchase price with semiannual payments over the next 5 years. The interest rate on the debt is 10%, compounded semiannually.

(b) Find the total amount paid for the purchase.

Answer 1

Given the following information,

Purchase price of house = $340,000

Down payment = $150,000

Balance amount = Purchase price of house - Down payment

Balance amount = 340,000 - 150,000

Balance amount = 190,000

We know that

Semi annual payment = P*(r/m)/ (1-(1+(r/m))^(-m*t))

Where,

P = loan amount = 190,000

r = 10% = 0.10

m = semi annual payments = 2

t = 5 years

Substituting the given values in the above equation, we get

Semi annual payment = 190,000*(0.10/2)/ (1-(1+(0.10/2))^(-2*5))

Semi annual payment = 190,000*(0.05)/ (1-(1+(0.05))^(-10))

Semi annual payment = 190,000*(0.05)/ (1-(1.05)^(-10))

Semi annual payment = 9500/ (1 - 0.6139)

Semi annual payment = 9500/ 0.3861

Semi annual payment = 24605.869

Amount to be paid in 5 years = Semi annual payment*m*t

Amount to be paid in 5 years = 24605.869*2*5

Amount to be paid in 5 years = 246058.69

Total amount paid for the purchase = Amount to be paid in 5 years + Down payment

Total amount paid for the purchase = 246058.69 + 150,000

Total amount paid for the purchase = 396058.69

Therefore, total amount paid for the purchase is $3,96,058.69