Question

3. A car is financed for $30,000 for a period of 4 years at annual percentage rate of 8%. Determine a) the uniform equal monthly payment for the car b) the amount owed at the end of the first year c) the extra monthly payment that must be made if the car was the paid off a the end of three years

Answer 1

Total amount of loan = $30,000

Rate of interest = 8%

Time = 4 years

Total amount to be repaid after 4 years = P(1 + r)ⁿ

Where P is the amount borrowed, r is the rate of interest and n refers to the number of periods.

Putting the values:

Amount to be repaid = 30,000(1 + 0.08)⁴

= 30,000(1.08)⁴

= 40,814.669

(a) Since there are 48 months in four years, the equal monthly payments equal:

$\fn_phv \frac{40,814.669}{48}=850.3056$

So, equal monthly payments are equal to $850.31 (approximately).

(b) Amount repaid in first year equals:

Monthly payment $\fn_phv \times$ Number of months in a year

850.3056 $\fn_phv \times$ 12 = $10,203.67 (approximately)

Amount owed at the end of the first year:

Total amount to be repaid - Amount repaid in first year

40,814.67 - 10,203.67 = 30,611 (approximately)

(c) Total amount to be repaid if the loan was to be paid off in three years = 30,000(1.08)³ = 37,791.36.

Monthly payment can be calculated by dividing the total amount to be repaid by the total number of months in three years:

$\fn_phv \frac{37,791.36}{36}= 1049.76$

So, the difference between the monthly payment equals 1049.76 - 850.3056 = 199.45 (approximately).