she will make 12 semi-annual payments at the end of each six months starting at the end of 2 years.
you can use the following calculator to solve this.
https://arachnoid.com/finance/index.html
the results of using this calculator are shown below:
the first analysis shown below found the future value of 400,000 for 8 semi-annual periods.
inputs were everything but future value.
output was future value.
the second analysis shown below took the future value from the first analysis and made it the present value.
it then calculated the semi-annual payments required to satisfy the loan.
inputs were everything but payment.
output was payment.
the third analysis shown below is the results of doing an excel analysis to show the semi-annual period by period transactions.
terms in this display are:
sair - semi-annual interest rate.
eosap1 - end of semi-annual period 1 - shows all the time period from start to finish. time period 0 to 4 is involved in the first analysis. time period 5 through 17 is involved in the second analysis.
eosap2 - end of semi-annual period 2 - shows the time periods from the second analysis.
rembal - remaining balance in the account
note 1 - the future value from the first analysis becomes the present value of the second analysis.
note 2 - the remaining balance in the account becomes 0 when all the semi-annual payments are made.
the calculator uses 2% as the interest rate per semi-annual time period.
excel uses .02 as the interest rate per semi-annual time period.
rate = percent / 100.
percent = rate * 100.
the procedure in excel is as follows;
for semi-annual period 1 to 4, the remaining balance in the current time period is equal to the remaining balance in the previous time period multiplied by 1.02
for semi-annual periods 5 to 17, the remaining balance in the current time period is equal to the remaining balance in the previous time period multiplied by 1.02 and then having the semi-annual time period payment of 40,941.74 subtracted from it.
let me know if you have any questions,.
theo