Malorie took out a loan to build a deck.The loan was for $15000 and had a 7.5% simple interest rate. If she paid a total of $1,687.50 in int

Question

Malorie took out a loan to build a deck.The loan was for $15000 and had a 7.5% simple interest rate. If she paid a total of $1,687.50 in interest,how long did she have the loan?

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Kylie 2 weeks 2021-09-13T22:26:34+00:00 1 Answer 0

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    2021-09-13T22:28:22+00:00

    Answer:

    • The final value (FV) ┬áthat is paid in a loan (which is the sum of the capital and the interests) equals the present value (PV) of the loan ┬ámultiplied by (1+i\times{n}), in a simple interest context, where “n” equals the periods of time and “i” equals the interest rate valid for that periodicity.
    • Then FV=PV\times(1+i\times{n}). In this case, PV=$15,000; final value equals FV=$15,000+1,687.5= $16,687.5.
    • We should clear “n” from our equation, which means: 16,687.5=15,000\times(1+n\times0.075). Dividing both sides by 15,000, then subtracting 1 both sides, and finally dividing by 0.075 both sides, results in n=1.5.
    • Then, Malorie had the loan for one an a half periods.

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