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.