Question

Mantago wants to borrow $20,000 to buy a used car. He examined his budget and decides that he can afford a payment of $425 a month. If his bank offers him an APR of 7.5%, how long should he borrow the money so he can afford his monthly payment?

3.5 years
4.66 years
4.5 years
4 years

Answer 1

I think it’s 4.66 years

Answer 2

4.66 years

Explanation:

Let us assume that it will take 't' years for him to repay the money that he would borrow.

We can use monthly cashflow formula:

`C=Pr((1+r)^(12t))/((1+r)^(12t)-1)`

Here, we have been given:

Monthly cashflow C=425

Loan amount P=20000

Interest rate AMR = 7.5%. Therefore, we have
`r=(0.075)/(12)`

Upon substituting these values in the formula, we get:

`425=20000\cdot (0.075)/(12) ((1+(0.075)/(12))^(12t))/((1+(0.075)/(12))^(12t)-1)`

Upon simplifying, we get:

`425=125 ((1+0.00625)^(12t))/((1+0.00625)^(12t)-1)`

`425=125 ((1.00625)^(12t))/((1.00625)^(12t)-1)`

Upon solving this equation using a calculator, we get:

`t=4.66`

Therefore, correct answer is 4.66 years. That is, second choice from the given options.