Question

John Fare purchased $24,000 worth of equipment by making a $4000 down payment and promising to pay the remainder of the cost in semiannual payments over the next 5 years. The interest rate on the debt is 10%, compounded semiannually. Find the following. (Round your answers to the nearest cent.) b) the total amount paid over the life of the loan $

Answer 1

Purchase Price of Equipment is $ 24000 and down payment is $ 4000.

Therefore Loan Amount = 24000-4000

= $ 20000

Calculation of Semi Annual Payments of Loan over next 5 years @ 10%.

Semi Annual Payment = Loan Amount/ PVAF(r%, n period)

PVAF(r%, n period) is the annuity factor where r% is the semi annual rate and n means number of semi annual period i.e. 10

PVAF(5%, 10 period) = (1+r%)ⁿ-1/ (r%* (1+r%)ⁿ)

= (1+5%)¹⁰-1/(5%*(1+5%)¹⁰)

=(1+0.05)¹⁰-1/(0.05*(1+0.05)¹⁰)

= 1.628894627-1/(0.05*1.628894627)

= 0.628894627/0.081444731

=7.7217

Therefore

Semi Annual Payment = 20000/7.7217

= $ 2590.10 approx

Total amount Paid over Loan = Semi Annual Payment* Number of Semi Annual Payment

=2590.10*10

=$ 25901