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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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syed514
Total payable amount = (10000){1 + 0.11}^5 = 16850.5815 ;
Total interest = 16850.5815 - 10000 = 6850.5815.
Total interest for 5 years = (0.11 X 10000 X 5) = 5500.
hope it helps
nobillionaireNobley
The present value of an annuity is given by PV = P(1 - (1 + r)^-n)/r; where P is the periodic (monthly) payments, r is the interest rate = 0.11/12 = 0.009167 and n is the number of periods = 5 x 12 = 60.

10000 = P(1 - (1 + 0.009167)^-60)/0.009167
P = 91.67/(1 - 0.578386) = 91.67/0.421614 = 217.43

Sammy makes a monthly payment of $217.43. In 5 years, the total payment will be 217.43 x 60 = $13,045.80
Therefore, total interest paid = $13,045.80 - $10,000 = $3,045.80 ≈ $3,046

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