# Inflation-complicated compound interest

1. Jan 7, 2009

### NicholasMM

Hi gang, I need help with a formula if somebody with an enormous brain and generous heart has some spare time.

I need to work out what 9% of $60,000 ($5400) invested annual at 7% (net of fees and taxes) would grow to in 30 years, with the $60,000 increasing by 3% inflation each year (so the figure that 9% amounts to grows each year). There is also a starting balance of$100,000.

I then need to be able to alter that 9% and make it 12% to see what the difference would be in the result.

If anybody can help a maths knucklehead such as myself that would be wonderful.

Thanks ... Nick.

2. Jan 7, 2009

I don't think I understand the statement of the problem. Are you looking for the nominal or the real amount? Is 3% the inflation rate -- because in the problem it sounds like a COLA? What is the $100,000 starting amount -- does it include the$60,000 or not? If so, what happens with the other $40,000, is it invested at the risk-free rate (which is what?)? 3. Jan 7, 2009 ### NicholasMM Hi CR, I didn't explain myself very well. In Australia, we have compulsory retirement savings of 9% of our annual wage ($60,000 in my example).

I'm trying to work out what those contributions would grow in 30 years, given 7% returns (for simplicity, net of fees and taxes) a year and, critically, with the annual wage (again, $60, 000 in my example) rising each year in line with inflation of 3%pa, so that the 9% compulsory amount increases too each year. I then want to change the 9% to 12% to compare how tipping in each year an amount extra to the compulsory 9% would effect the result (that is, the investment balance). The$100,000 would be the retirement account balance when the retirement investor switched from 9% of annual wage to 12%.