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3 September, 09:58

Melissa wants to buy a living room set that cost $1800. She could get a 3-year personal loan from a bank at a simple interest rate of 8.7%. She could also get a 3-year loan from a finance company that charges 8.5% compounded annually. Which answer correctly compares the total cost of the loan with simple interest and the loan with compound interest?

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  1. 3 September, 12:43
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    The total cost of the loan with simple interest $2269.8 is less than the loan with compound interest $2299.12.

    Explanation:

    Simple Interest (I) = Principal (Loan) * Time*Rate : 100

    Loan = $1800

    Time = 3 years

    Rate = 8.7%

    I = 1800*3*8.7/100 = $469.8

    Total cost of loan with simple Interest = loan + simple interest = $1800 + $469.8 = $2269.8

    Compound interest = [Loan (1+r) ^n] - Loan

    Loan = $1800

    r is annual interest rate = 8.5% = 0.085

    n is duration of the loan = 3 years

    Compound interest = [1800 (1+0.085) ^3] - 1800 = 2299.12 - 1800 = $499.12

    Loan with compound interest = 1800 + 499.12 = $2299.12
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