Question

Sam really wanted to buy a car, but did not have the money at the moment. He was talking to the salesman and they said that he could get him a loan for the car for $30,000 on a 11.41% per year interest rate compounded continuously. He wanted to spend his money on other things so he held off on paying down the balance of the loan for a while. 1. What was the loan balance 3 months in? 2. Sam has a take home pay of $40,000 a year. What percentage of his take home pay is the interest on the loan in his first year?

Answer 1

1) $30,821 ( loan balance after 3 months in )

2) 8.56%

Explanation:

Final Amount of compound interest: A = P ( 1 + i ) ^ n

p = principal = $30,000

r = interest rate = 11.41% = 0.1141

n = number of years

1) Loan balance after 3 months

n = 3/12 = 0.25 years

A = 30,000 ( 1 + 0.1141 ) ^ 0.25

= $30,821 ( loan balance after 3 months in )

2) Loan Balance after 1 year

A = 30,000 ( 1 + 0.1141 ) ^ 1

= $33423

interest on loan = 33423 - 30,000 = $3423

percentage of $40,000 is $3423

= 3423 / 40,000 * 100

= 8.56%