Question

Mr. Doe de Tal Perencejo paid an early $ 2000 for the purchase of a car Then he paid S200 per month for 36 months at an interest of 12% per year compounded monthly to pay the rest of the cost of the car

a. What Was it the original cost of the car?

b. What proportion of the payments are interest charges?

Answer 1

(a) Original cost of the car will be the early payment i.e. $2000 plus the present value of $200 per month for 36 months.

Original cost of the car = $2000 + Present value of $200 for 36 months

Calculation of present value of payments:

Here, the payments  will be same every month, so it is an annuity. For calculating the present value of annuity, we will use the following formula:

PVA = P * (1 - (1 + r)^-n / r)

where, PVA = Present value of annuity, P is the periodical amount = $200, r is the rate of interest =12% compounded monthly, so monthly rate = 12% 12 = 1% and n is the time period = 36 months

Now, putting these values in the above formula, we get,

PVA = $200 * (1 - (1 + 1%)^-36 / 1%)

PVA = $200 * (1 - ( 1+ 0.01)^-36 / 0.01)

PVA = $200 * (1 - ( 1.01)^-36 / 0.01)

PVA = $200 * (1 - 0.69892494962) / 0.01)

PVA = $200 * (0.30107505037 / 0.01)

PVA = $200 * 30.1075050373

PVA = $6021.5

So, present value of payments = $6021.5.

Now,

Original cost of the car = $2000 + $6021.5 = $8021.5

(b) Total payment = $2000 + ( $200 * 36)

Total payment = $2000 + $7200 = $9200

Interest charges= Total payment - original cost

Interest charges = $9200 - $8021.5 = $1178.5

Proportion of interest charges in total payment = Interest charges / Total payments * 100

Proportion of interest charges in total payment = $1178.5 / $9200 * 100 = 12.81%