You want to have an income of $50,000 per year in retirement, and you think you will be alive for 30 years in retirement. How much do you need to have invested the day you retire, in real dollars, assuming a 3% real rate of return?

Question

You want to have an income of $50,000 per year in retirement, and you think you will be alive for 30 years in retirement.  How much do you need to have invested the day you retire, in real dollars, assuming a 3% real rate of return?

I just need to make sure I'm doing this right.. I'm worried I'm not handling the r right. Does "real rate of return" = r?

PVA = ?
FV = 50,000 a year
r = .03 
n= 30

PVA = 980,022.07

MathMate · Answer

Yes, your answer is correct, as follows.

P=A[P/A,0.03,30]
=50000[P/A,0.03,30]
=50000((1+0.03)^30-1)/(.03*(1+0.03)^30)
=980022.067

As for the interest, there is no mention of the compounding rate, and 3% is qualified as "real" rate or return, or EAR (effective annual rate), whatever the APR might be. So using 3% as EAR is correct.