# I need help financing my retirement

I am a graduated Finance major but I am stuck financing my own retirement.

Between the ages of 25 and 68, in which I would deposit 25% of my income each year. The income starts at \$80,000 with an annual growth rate of 5% and assuming an interest rate of 2%. (I think that’s fair) I will be assuming for simplicity that I will receive my first salary (\$80,000) when I turn 25, and my last salary when I turn 68. As soon as I receive a salary, I will save 25% of it.

I would like to know (1) how much I will have in my retirement account when I turn 68, immediately after the last deposit, and (2) what single deposit made on my 25th birthday would give the same account balance when I turn 68. I am trying to apply the idea of present value.

But this raises issues, as if I try to use the equation for the present value of a growing annuity with a 5% growth rate and 2% discount rate, r-g will yield a negative number. Also, I could not find online how to do this on my HP 10bII+ financial calculator and I don’t want to manually enter 44 payments.

Thank you if you read that.

This is one example why one should understand the theory and not just memorize formulas, which may not work on every case. For this problem, all you have to do is draw a time diagram and make a summation.

Assuming you earn 80,000 at age 25, the income grows by 5% and the interest remains constant at an annual effective rate of 2%, if you deposit 1/4 of your income each year (and assuming i didn’t make a calculator mistake):
the present value of this amount at age 25 is 1,754,616.238, or about 1.755 million
the value of this amount at age 68 is 4,111,398.093, or about 4.111 million

^ Nicely done!!!

On the BA II (should work similarly for the HP):

P/Y=C/Y=1
Set BGN mode
N 44 I -2.857142 PMT -20000 CPT PV 1,754,616.238

I = (0.02 - 0.05)/(1 + 0.05)