TVM tricky question I am confused about


Gerard Jones plans to save for his 5-year doctorate degree, which starts 6 years from now. The current annual expenditure is $7,200 and it is expected to grow by 7 percent annually. Gerard will need to make the first payment 6 years from today. He identifies a savings plan that allows him to earn an interest of 8 percent annually. How much should Gerard deposit each year, starting one year from today? Assume that he plans to make 5 payments.

A. $8,370.
B. $8,539.
C. $8,730

this is a standard annuity problem. just start by drawing a time diagram with all the cashflows.

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I second the timeline recommendation. If you don’t project the tuition payments correctly, you will not get the correct answer.

Hint: I would use time t=5 for all the accumulations and discounting. If you get the PV(tuition payments) at time 5, you can set it equal to the FV of the deposits.

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It turns out that this was already asked in a thread from 2018, so I’ll just throw in the BAII steps

The twist here is that to get the PV of the tuition payments at time 5, the interest rate you will use is 0.08 - 0.07/(1+0.07) = 0.934579439% to account for the tuition growth rate and nominal discounting. Also, I use an immediate annuity PV at time 5 with the time 5 tuition amount of 10,098.37246 (you could also use an annuity due with the time 6 tuition amount, but then you have to do all calcs as of time 6)

N=5, I= 0.934579439, PMT = 10098.37246 CPT PV -49106.50623

N=5 I=8 FV = 49106.50623 CPT PMT -8370.520948

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