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?

Answer 1

• 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
  `(1+i*{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*(1+i*{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*(1+n*0.075)`. 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.