Find the Loan Amount for the amortized loan.

Question

Find the Loan Amount for the amortized loan.

If Peter can afford car payments of $255 per month for 4 years, what is the price of a car that he can afford now? Assume an annual interest rate of 11%.

Answer 1

We need to know how often the interest is compounded...

Annually, semiannually, quarterly, or monthly..

 

However, I will do this assuming monthly compounding just to show how.

 

1)  The total Peter can pay is $255 per month for 4 years.

     That is 48 monthly payments of $255

     255(48) = $12,240 total pay off amount including interest

 

Compound interest formula

A = P(1+r/n)^nt

A = final amount = 12240

p = initial investment (to be determined)

r = interest rate as decimal = .11

n = number of times compounded per year = 12

t = time in years = 4

 

12240 = p(1 + .11/12)¹²⁽⁴⁾

 

P = 12240/(1 + .11/12)⁴⁸

 

P = $7898.82

 

He can afford to buy a car that costs $7898.82 assuming

interest is compounded monthly.

 

If the compound period is different just change the value of "n"

in the equation and rework.

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For interest compounded annually:

 

12240 = p(1+.11)⁴

p = 12240/(1.11)⁴

p = $8062.87

if interest is compounded only once per year (annually)