Question

John Fare purchased $6,000 worth of equipment by making a $1000 down payment and promising to pay the remainder of the cost in semiannual payments over the next 6 years. The interest rate on the debt is 12%, compounded semiannually. Find the following. (Round your answers to the nearest cent.) (a) the size of each payment $ Correct: Your answer is correct. (b) the total amount paid over the life of the loan $ Incorrect: Your answer is incorrect. (c) the total interest paid over the life of the loan

Answer 1

Answer:

C $ 596.39

total payment          7,156.68

Interest expense     2,156.68

Explanation:

6,000  -  1,000 = 5,000 amount to finance

We will calcualte the cuota of an annuity of 6 years with semianual payment at 12% annual rate.

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV  $5,000.00

time   12 (6 years times 2 payment per year)

rate            0.06 (12% annual we divide by 2 to get semiannual)

$5000 \times \frac{1-(1+0.06)^{-12} }{0.06} = C$

C $ 596.39

The total amount paid will be the cuota times the time of the loan:

Total amount paid

596.39 x 12 = 7,156.68‬

The interest will be the difference between the total amount paid and the principal of the loan

Interest paid

total payment          7,156.68

principal                 (5,000)

Interest expense     2,156.68