The high impact of the real interest rate

July 18th, 2012
money  [html]
If you're a young person trying to decide how much to save for retirement, a big thing to consider is how much the money you invest now will be worth then. I've heard wildly different claims about this, from it being worth twice as much to twenty times as much! If I'm trading off between spending money now and spending money in 40 years, a big consideration is how much my saving helps my 40-years-older self.

A key number here is the real interest rate. That's how much money you expect to earn after subtracting inflation. If you're earning 7% that means \$100 today is nominally \$107 [1] next year, but if inflation is 3% then that \$107 is really only going to be worth \$104 [2] in today's money. So the real interest rate is 4% [3].

Small changes in the real interest rate have a large effect on how much money you have at retirement. I have about 40 years of working life ahead of me, which means money I invest now has about 40 years to grow before I need it. So how much money does \$100 invested now bring me in 40 years? It depends on the real interest rate:

real interest rate money after 40 years -1% 0.67x -0.5% 0.82x -0.2% 0.92x 0% 1.00x 0.2% 1.08x 0.5% 1.22x 1% 1.49x 2% 2.21x 3% 3.26x 4% 4.80x 5% 7.04x 6% 10.29x 7% 14.97x 8% 21.72x 9% 31.41x 10% 45.26x `x` `x^40`
At low interest rates there's some advantage to investing now instead of just saving money near retirement, but at higher ones the advantage is very large. It's worth it to put in a lot of effort on figuring out what you the real interest rate will be instead of just choosing the first number you find that looks plausible. The value of information here is high.

Over the course of your career the money you save for retirement has less and less time to grow. This same table computed for 20 years growth, is:

real interest rate money after 20 years -1% 0.82x -0.5% 0.90x -0.2% 0.96x 0% 1.00x 0.2% 1.04x 0.5% 1.10x 1% 1.22x 2% 1.49x 3% 1.81x 4% 2.19x 5% 2.65x 6% 3.21x 7% 3.87x 8% 4.66x 9% 5.60x 10% 6.73x 11% 8.06x 12% 9.65x `x` `x^20`
If you expect a high interest rate it makes sense for you to try really hard to save money now, and save somewhat less as you approach retirement. While if you expect a low interest rate it matters much less when you save.

[1] `7% * \$100 + \$100`

[2] `(7% - 4%) * \$100 + \$100`

[3] `7% - 4%`

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