Question

While Mary Corens was a student at the University of Tennessee, she borrowed $12,000 in student loans at an annual interest rate of 10.10%. If Mary repays $1,500 per year, how long (rounded up to the nearest year) will it take her to repay the loan?

Answer 1

Step-by-step explanation:

we need to sovle for the time in an ordinary annuity.

The loan (present value of the annuity) is 12,000

the payment are 1,200 per year

and the rate is 10.10% we need to solve for years:

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C $ 1,500

time n

rate 10.10% = 10.10/100 = 0.101

PV $ 12,000

`1500 * (1-(1+0.101)^(-n) )/(0.101) = 12000\\`

we plug the values and work-out the equation

`(1+0.101)^(-n)= 1-(12000*0.101)/(1500)`

Solve for the right side, and apply logarithmics properties:

`(1+0.101)^(-n)= 0.192\\`

-n = -17.15110682

n = 17.15

the loan will take 17 years to repay if Mary does annual payment of 1,500