Question

A man buys a car for $33,000 with no money down. He pays for the car in 48 equal monthly payments with interest at 9% per annum, compounded monthly. What is his monthly loan payment?

Answer 1

Answer:

Man has to pay $1921.19 per month.

Step-by-step explanation:

The formula of Compound Interest is:

$A = P(1+\frac{r}{n})^{nt}$

where A = Amount

P = Principle

r = rate

n = Number of Compounding per year

t = total number of year

Here, A = 33,000, r = 9% = 0.09, n = 12(monthly), and t = 48(48 months).

Putting all these values in above formula:

$33000 = P(1+\frac{0.09}{12})^{12\times4}$

⇒ $33000 = P(\frac{12.09}{12})^{48}$

⇒ $33000 = P(1.0075)^{48}$

⇒ $33000 = P(1.4314)}$

⇒ P = 33000 ÷ 1.4314 = 23054.35

Monthly payment = 23054.35 ÷ 12 = 1921.19

Hence, Man has to pay $1921.19 per month.