Using present value and future value to determine repay

Question

Farnaz must repay her $17000 student loan. She can afford to make monthly payments of $325. The bank's interest rate is 7.2% compounded monthly. Determine how long it will take Farnaz to repay her loan.

 

 

Answer 1

Let's do a little formula work

 

P = iPV/(1-(1+i)^-n)

 

doing algebra will lead you to this result

 

n = -ln(PV/p*i - 1)/ln(1+1)

 

the interest rate i in this example is .072/12 = .006

 

Plug in the numbers

 

-ln(17000/325*.006 - 1)/ln(1.006)

 

193.72 periods or 16 years and 2 months with the final payment being a partial payment.