the interest rate on her loan is 3.8% per year.
if she agrees to a 6 year repayment plan, then her monthly payments will depend on whether she starts paying off the loan right away, or she starts paying the loan after she graduated.
assuming she can't start paying off the loan until after she graduates and gets a job, then the following most likely applies.
the loan period is 8 years.
this consists of 2 years where no payments are made followed by 6 years where the loan is paid off in monthly amounts at the end of each month of the 6 year payment period.
the future value of 5,000 at 3.8% per year compounded monthly would be equal to 5000 * (1 + .038/12)^24 = 5394.165101.
the monthly payments for 6 years at 3.8% per year would be equal to 83.90203696 payable at the end of each month after the loan starts.
the detailed monthly cash flows are shown in the following excel printout.
there are no payments for the first 2 years of the loan.
then they are 6 years of monthly payments of 83.90203696 dollars per month, which is normally rounded off to the nearest penny to be equal to 83.90 at the end of each month.
the value of the loan at the end of 2 years with no payments is 5000 * (1 + .038/12) ^ 24 = 5390.165101.
this is the amount of the loan that needs to be paid off in 6 years.
the monthly amount was derived by use of a financial calculator, such as the one found at https://arachnoid.com/finance/
these are the inputs.
this is the output.
you can see that the monthly payments are shown at 83.90.
i didn't use this calculator, but used a comparable calculator, called the TI-BA-II.
that shows the results in a little more detail, but the results from both are effectively the same, except that the results from the online calculator have been rounded as shown.
inputs to the online financial calculator are:
present value (PV) = -5394.165102
future value (FV) = 0
number of monthly time periodws (NP) = 6 * 12 = 72
payment amount (PMT) = what you want the calculator to tell you.
interest Rate per period, % = 3.5/12 = .3166666667
payments to be made at end of period.
after the inputs are made, then click on PMT and the calculator tells you what the monthly payment will be.
the excel printout shows the detailed month by month transactions.
at the end of the 8 years, the remaining balance on the loan is 0, as it should be.
this can also be solved using the following formula.
ANNUITY FOR A PRESENT AMOUNT WITH END OF TIME PERIOD PAYMENTS
a = (p*r)/(1-(1/(1+r)^n))
a is the annuity.
p is the present amount.
r is the interest rate per time period.
n is the number of time periods.
in your problem:
p = 5394.165101
r = .038/12 = .003166666667
n = 6 * 12 = 72
the formula becomes:
a = (5394.165101*.003166666667)/(1-(1/(1+.003166666667)^72)).
use your scientific calculate and make your entries exactly as shown and you should get a = 83.90203696.
this formula is one of a bunch of financial formula that can be found at https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#f9
use of a financial calculator is a lot easier.