Here is a question I had from a mock exam this weekend
-Three years from now, an investor will deposit the first of eight $1,000 payments into a special fund. The fund will earn interest at the rate of 5% per year until the third deposit is made.
-Thereafter, the fund will return a reduced interest rate of 4% compounded annually until the final deposit is made. How much money will the investor have in the fund at the end of ten years assuming no withdrawals are made?
A: The total value in the fund at the end of the fifth year is $3,152.50: PMT = -1,000; N = 3; I/Y = 5; CPT → FV = $3,152.50. (calculator in END mode)
The $3,152.50 is now the present value and will then grow at 4% until the end of the tenth year. We get: PV = -3,152.50; N = 5; I/Y = 4; PMT = -1,000; CPT → FV = $9,251.82
If I draw a timeline, I have the 3 payments starting three years from now. So if we follow the answer, there are the periods between t0 and t3 that haven’t been accounted for by proper discounting in this question’s answer.
I understand that N=3 for the three payments that first occur, and then N=5 for the following payments. But at some point here don’t we need to discount the end-value since the first of eight payments begins in three years and not at the end of year 1?