Question

A student loan paid faithfully for 23 years had the following statistics: Borrowed: $26,400 Paid back to date: $32,700 Still Owes: $45,276.63

Monthly Payment : 282.524

Annual Rate of Interest : 12%

Given her monthly payment, how long will it take for the student to pay their loan back?

What amount of monthly payment would have allowed the student to pay their loan back in 23 years? (Hint: You can either use Excel’s PMT function to answer this or guess and check. For the guess and check approach, pick a constant monthly payment for 276 months, compute the present value of each payment using the monthly interest rate, and ensure that the sum of these 276 present values exactly equals the amount of the loan.)

Answer 1

Answer : Calculation of Period  it will take for the student to pay their loan back:

Using NPER function of excel :

=NPER(rate,pmt,pv,fv)

wher

rate is the rate of interest per period i.e 12% / 12 = 1% (Divided by 12 as monthly payments)

pmt is periodic monthly payment i.e 282.524

pv is the amount still owes i.e 45276.63

fv is 0

=NPER(1%,282.524,-45276.63,0)

Therefore Number of Months is 96.13 months or 7 years

Calculation of Periodic Monthly Payment

=PMT(rate,nper,pv,fv)

rate is the rate of interest per period i.e 12% / 12 = 1% (Divided by 12 as monthly payments)

nper is the number of payments i.e 23 * 12 = 276

pv is the amount borrowed + Paid to date i.e 26400 + 32700 = 59100

fv is 0

=PMT(1%,276,-59100)

Periodic Payment is 591