Sam would like to buy a car. The best offer that Sam is able to get for loan is 4.8% compounded monthly for a term of 60- months. Sam has a $2500.00 as a down p

Question

Sam would like to buy a car. The best offer
that Sam is able to get for loan is 4.8%
compounded monthly for a term of 60-
months. Sam has a $2500.00
as a down payment and can afford a monthly
payment of $300.00. Under these conditions,
find the price (inclusive of all the taxes)
that Sam can buy.

Answer 1

The equation for total repayment amount for a loan with monthly compounded interest is:

 

T=P*(1+r/n)^n*t

 

where:

T=total amount

P=principal

r=annual interest rate

n=frequency of compounding per year

t=number of years

 

in this case:

r=0.048

n=12

t=5

 

and the equation is: T=P*(1.004)^60

 

Now we need to calculate T which is the total amount that Sam can afford to pay over the 60mo term of the loan. He can afford $300 a month:

 

T=300*60=$18,000

 

So plug in T and solve for P, the initial loan amount:

 

18000=P*(1.004)^60

P=14,166.08

 

So that's the max loan amount that Sam can borrow to buy a car. Now add the down payment to get total price of the car:

 

14166.08+2500=$16,666.08