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

Answer:

4.66 years

Step-by-step 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:

$C=Pr\frac{(1+r)^{12t}}{(1+r)^{12t}-1}$

Here, we have been given:

Monthly cashflow C=425

Loan amount P=20000

Interest rate AMR = 7.5%. Therefore, we have $r=\frac{0.075}{12}$

Upon substituting these values in the formula, we get:

$425=20000\cdot \frac{0.075}{12} \frac{(1+\frac{0.075}{12})^{12t}}{(1+\frac{0.075}{12})^{12t}-1}$

Upon simplifying, we get:

$425=125 \frac{(1+0.00625)^{12t}}{(1+0.00625)^{12t}-1}$

$425=125 \frac{(1.00625)^{12t}}{(1.00625)^{12t}-1}$

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.