The problem describes a debt to be amortized.
A man buys a house for $350,000. He makes a $150,000 down payment and amortizes the rest of the debt with semiannual payments over the next 12 years. The interest rate on the debt is 11%, compounded semiannually. (Round your answers to the nearest cent.)
(a) Find the size of each payment.
$ 1
(b) Find the total amount paid over the life of the loan (including the down payment).
$ 2
(c) Find the total interest paid over the life of the loan.
$ 3
To find the size of each payment (a), total amount paid over the life of the loan (b), and total interest paid over the life of the loan (c), we can use the formula for amortized payments.
The formula for calculating an amortized payment is:
P = (r * A) / (1 - (1+r)^(-n))
Where:
P is the size of each payment
r is the interest rate per period (semiannual in this case)
A is the initial loan amount
n is the total number of payment periods
(a) To find the size of each payment, we need to know the total number of payment periods. In this case, the loan is amortized over 12 years with semiannual payments. There are 12 years * 2 payments per year = 24 payment periods.
Plugging the values into the formula:
P = (0.11 / 2 * (350,000 - 150,000)) / (1 - (1 + 0.11 / 2)^(-24))
Simplifying:
P = 8,894.01
Therefore, the size of each payment (a) is $8,894.01.
(b) To find the total amount paid over the life of the loan, we simply multiply the size of each payment by the total number of payments:
Total Amount Paid = P * n
Plugging in the values:
Total Amount Paid = 8,894.01 * 24 = $213,456.24
Therefore, the total amount paid over the life of the loan (including the down payment) (b) is $213,456.24.
(c) To find the total interest paid over the life of the loan, we subtract the initial loan amount from the total amount paid:
Total Interest Paid = Total Amount Paid - A
Plugging in the values:
Total Interest Paid = 213,456.24 - 200,000 = $13,456.24
Therefore, the total interest paid over the life of the loan (c) is $13,456.24.