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?
The final value (FV) that is paid in a loan (which is the sum of the capital and the interests) equals the present value (PV) of the loan multiplied by [tex](1+i\times{n})[/tex], in a simple interest context, where "n" equals the periods of time and "i" equals the interest rate valid for that periodicity.
Then [tex]FV=PV\times(1+i\times{n})[/tex]. 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: [tex]16,687.5=15,000\times(1+n\times0.075)[/tex]. 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.
