Sammy borrowed $10,000 to purchase a new car at an annual interest rate of 11%. She is to pay it back in equal monthly payments over a 5-year period. How much total interest will be paid over the period of the loan? Round to the nearest dollar.

Question

Mathematics

Kolton Wilkinson

4 May, 07:03

Sammy borrowed $10,000 to purchase a new car at an annual interest rate of 11%. She is to pay it back in equal monthly payments over a 5-year period. How much total interest will be paid over the period of the loan? Round to the nearest dollar.

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Answers (1)

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Stevenson · Answer 1

First we need to find the monthly payments in order to find the interest

Use the formula of the present value of an annuity ordinary which is

Pv=pmt [ (1 - (1+r/k) ^ (-kn)) : (r/k) ]

Pv present value 10000

PMT monthly payment?

R interest rate 0.11

K compounded monthly 12 because the payments to repay the loan are monthly

N time 5years

Solve the formula for PMT

PMT=pv:[ (1 - (1+r/k) ^ (-kn)) : (r/k) ]

PMT=10,000: ((1 - (1+0.11:12) ^ (

-12*5)) : (0.11:12))

=217.42 per month

After that find total paid amount

5years=60 months

Total paid=217.42*60=13,045.2

Total interest

13,045.2-10,000=3,045.2. Answer