Inflation-complicated compound interest

[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.

 

[CRGreathouse]

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?)?

 

[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%.

I know how to work out the FV of $5400 (9% of $60,000) invested at 7% for 30 years. What I don't know is how to do is allow for the $5400 to increase each year in line with inflation.

I'd really love it if you knew a formula for this that I could punch into google calc.

Thanks CR. I hope I haven't just made it much more confusing! ... Nick.

 

[CRGreathouse]

I know how to work out the FV of $5400 (9% of $60,000) invested at 7% for 30 years. What I don't know is how to do is allow for the $5400 to increase each year in line with inflation.

The easy way, then, is to divide everything by 1.03 each year so you're working in real (not nominal) terms. Thus you get 3.88% after-inflation returns (1.07/1.03 - 1) and your contribution stays at $5400 inflation-adjusted dollars.