Question

9. Suppose you take out a car loan for $9999 for 4 years at a 7.5% interest rate. What is your

Answer 1

Answer:

The monthly payment is $241.76.

Step-by-step explanation:

Given : Suppose you take out a car loan for $9999 for 4 years at a 7.5% interest rate.

To find : What is your monthly payment ?

Solution :

The formula to find monthly payment is  

$M=\frac{\text{Amount}}{\text{Discount factor}}$

Discount factor is $D=\frac{1-(1+i)^{-n}}{i}$

Substitute in the formula,

$M=\frac{A}{\frac{1-(1+i)^{-n}}{i}}$

$M=\frac{A\times i}{1-(1+i)^{-n}}$

where, A is the amount A=$9999

r is the rate =7.5%=0.075

$i=\frac{r}{12}=\frac{0.075}{12}=0.00625$

time t=4 years  

Time in months $n=t\times 12=4\times 12=48$

Substitute all the values in the formula,

$M=\frac{9999\times 0.00625}{1-(1+0.00625)^{-48}}$

$M=\frac{62.49375}{1-(1.00625)^{-48}}$

$M=\frac{62.49375}{1-0.7415101}$

$M=\frac{62.49375}{0.25848}$

$M=241.76$

Therefore, the monthly payment is $241.76.