Question

While buying a new car, Sophie made a down payment of $800 and agreed to make month-end payments of $270 for the next 4 years and 7 months. She was charged an interest rate of 2% compounded semi-annually for the entire term.

a. What was the purchase price of the car?

b. What was the total amount of interest paid over the term?

Answer 1

a.

2% compounded semi-annually means an effective rate of 2/2 = 1% per 6 months. The effective rate of interest per month becomes (1.01)^(1/6) - 1 = 0.165976% per month effective.

The purchase price of car will be sum of down payment and the present value of all future payments.

The present value of future payments can be found with the help of =PV function of Excel.

=PV(rate, nper, pmt)

where PV is present value

rate is effective rate of interest per period,

nper is number of periods,

pmt is periodic payment amount

A1 X ✓ fx =PV(0.00165976,55,270) B с D E F А -14181.12 1 2 3

Thus, =PV(0.00165976,55,270) comes out as $14,181.12. Ignore the negative sign of Excel as it shows cash flow signs are opposite. This amount of loan is taken (cash inflow) and pmt amount is repaid(cash outflow).

Monthly periods are taken into consideration.

Thus, the present value of all future payments is $14181.12.

Thus, price of car = Present value of future payments + Down payment

=14181.12+800 = $14981.12. This is the price of the car.

b.

The total amount of interest paid over the term = Total amount paid - amount of loan taken

=270*(12*4+7) - (14181.12-800)

The amount of loan is price of car less down payment

The total amount of interest paid over the term = 14850 - 13381.12 = $1468.88

Thus, interest paid is $1468.88.

Comment in case of any query.