money is worth 10.5% per year compounded monthly.
monthly payments are 7500.
the monthly payments will be for 48 months from the end of month 12 to the end of month 59.
the monthly interest rate will be 10.5/12 = .875%.
the present value of the payments will be equal to 292,930.08.
this present value will be at the end of the 11th month, since the first payment was at the end of the 12th month.
it needs to be brought back to the the beginning of the first month which is the end of month 0.
the present value will be 292,930.08 divided by 1.0875 ^ 11 = 266,161.32.
i used the ti-ba-ii calculator to get these results.
similar results can be obtained from the arachnoid online financial calculator at https://arachnoid.com/finance/index.html
i also used excel to confirm that what i did was correct.
here are the displays from the caclulator.
in the first calculator display, inputs were everything except present value.
output was present value.
in the second calculator display, the present value from the first calculator became the future value.
inputs were everything except present value.
output was present value.
here are the displays from excel.
in the excel displays, the first 11 months had zero investments.
the last 48 months had investments of 7500 each.
that took the 7500 investments from end of month 12 to end of month 59.
this would be first investment at end of month 12 + 47 additional investments that stop at end of month 59.
that was 11 months of no investments plus 48 months of 7500 investments.
the present value of that cash flow was brought back to end of month 0.
the present value of those cash flows confirmed the results from the financial calculator.
the growth factor for each month was (1 + .105/12).
the present value factor for each month was the cash flow for that month divided by (1 + .105/12) ^ (end of month).
for example, the present value of 7500 invested at the end of the 12th month was 7500 / (1 + .105/12) ^ 12 = 6755.518547, as shown in the excel display.
let me know if you have any questions.
theo