the interest rate is 4% per year compounded semi-annually.
she starts payment at the end of 2 years.
calculator to use online is https://arachnoid.com/finance/index.html
using my ti-ba-ii business analyst calculator, i do the following.
my calculator and the online calculator do the same thing, except that my calculator doesn't round the results to the nearest penny each time.
this could make a difference in the final result by a few pennies.
it's not enough to cause concern, except that your online problem solution might be affected by the small difference in results.
that's why i give you both, when there is a difference.
first i get the future value of 400,000 for 2 years at 4% compounded semi-annually.
inputs are:
pv = -400,000
fv = 0
np = 2 years * 2 = 4 semi-annual time periods.
ir = 4% per year / 2 = 2% per semi-annual time period.
pmt = 0
payments at end or beginning of each time period do not apply for this first analysis because there is no semi-annual payment involved.
output is fv = 432,082.974
that's how much is in the account at the end of 2 years.
that needs to be paid back in 12 equal semi-annual payments.
using the ti-ba-ii calculator again, inputs are:
pv = 432,082.974
fv = 0
np = 12 semi-annual time periods
ir = 2% per semi-annual time period
payment is made at the end of each semi-annual time period.
output is that a payment of 40,941.73937 needs to be paid at the end of each semi-annual time period for 12 semi-annual time periods.
that should be your solution.
ignore the negative and positive values.
they are required by the calculator, but can become confusing when dealing with two separate analyses, as was being done here.
here are the results from using the online financial calculator.
they will be very close to the results i got with the ti-ba-ii, if not right on.
the following excel spreadsheet printout shows the semi=annual period by semi-annual period remaining balances in the account.
the displays are rounded to the nearest penny, but the actual values used in the calculations are not rounded.
at the end of the loan period, the remaining balance is 0, as it should be.
your solution is that the periodic payment is equal to 40,941.74 when rounded to the nearest penny.