The Projected Annuity Amount Needed to Fund a Future- Annuity Inflow

Jill Grant is 22 years old (at t = 0) and is planning for her retirement at age 63 (at t = 41). She plans to save $2,000 per year for the next 15 years (t = 1 to t = 15). She wants to have retirement income of $100,000 per year for 20 years, with the first retirement payment starting at t = 41. How much must Grant save each year from t = 16 to t = 40 in order to achieve her retirement goal? Assume she plans to invest in a diversified stock- and- bond mutual fund that will earn 8 percent per year on average.

I solved like that:

step 1:

15 N

8 r

20000 CHS PMT

0 PV

FV = 54.304,23 (this would be the value in year 15 of what she saved in this first 15 years)

Than I had to knew tha value of the 100.000 PMT at T = 40, so I did:

100.000 CHS PMT

0 FV

20 N

8 r

PV = 981.814,74

than I had to go back 25 years with this value I got $ 143.362,53

as she alresy had money from the first saving (step 1) I had to do 143.362,53 - 54.304,23 = $89.058,30

Now this would be my PV and I need to go with this value in the future for 25 years with r=8 and ask the HP12c the

PMT = $8.342,87

The thing is that when I go to my calc to see if this is right I do:

N = 25

r = 8

PV = 89058,30 CHS

PMT = 8342,87 CHS

I get a FV = $ 1.219.826,912

Shouldn`t this FV be equal to $ 891.814,74??

Why It`s not?

I need help that was a really complex problem to solve, thanks.

In the last part, PV should be 54,304 instead of 89058. she actually has 54,304 saved up and needs a payment stream with a PV 89058 to accumulate to 981,814.

Nicely done with the calcs: they are all correct!!! :+1:

Hey Thanks a lot that explained, just one more question in the last equation that I did now changing the PV to $ 54.304, why in the calculator I need to do both positive or both with CHS? (when I enter the PV and the PMT in the calculator, If I do one signal and other the opposite I get dfferent answer)