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?
Accepted Solution
A:
Answer:Man has to pay $1921.19 per month.
Step-by-step explanation:The formula of Compound Interest is:
[tex]A = P(1+\frac{r}{n})^{nt}[/tex]
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:
[tex]33000 = P(1+\frac{0.09}{12})^{12\times4}[/tex]
⇒ [tex]33000 = P(\frac{12.09}{12})^{48}[/tex]
⇒ [tex]33000 = P(1.0075)^{48}[/tex]
⇒ [tex]33000 = P(1.4314)}[/tex]
⇒ P = 33000 ÷ 1.4314 = 23054.35Monthly payment = 23054.35 ÷ 12 = 1921.19Hence, Man has to pay $1921.19 per month.