Arithmetic Helps Solve Retirement Planning

The money you will have in the future is a function of four factors:

  1. Capital employed (C)
  2. Yield ((i)
  3. Marginal Tax Rate (MTR)
  4. Time. (n)

For single sum the future value is

Future value (FV) = C*(1+i*(1-MTR))^n. Capital times 1 plus yield after taxes to the power n

For capital $1,000, yield 5%, tax rate 30%, and 20 years you get $1,989.79

If you want to know the value of that you will add an inflation factor, r, Let’s say 2%.

The Future Value after inflation is FV/(1+r)^n or 1989.79 / (1.02)^20 =1,339.07

What that tells us

It is very difficult to build purchasing power.

.If you want to do better you have choices:

Have more capital, but that reduces spendable money today. You will be forced to balance current lifestyle with future lifestyle.

Improve the yield. That requires skills you may not presently have. Historically the stock market does better than the bond market, or bank deposits. In addition to skills you will need an attitude change to deal in the stock market. It is much more volatile and ups and downs trouble some people. Some people find rental income attractive. That requires skills and expenditure of time for maintenance and other duties. A business appeals to many but most are fulltime jobs with a side of investment.

Reduce the tax rate. Possible but not easy. Use containers like TFSAs, RRSPs, RESPs, when their characteristics match your purpose.

Start sooner. Compound growth doesn’t work like we think. More time has a significant effect. If you know how long it takes to double money, the rule of 72 says 72/i years, so at 5%,  72/5 = 14.4 years. You will find by starting early  you might get one more double.

It’s easier to see at high yield. At 12% money doubles about every six years. In 24 years you would have four doubles and in 18 years just three. The import thing to notice is the last double adds more income than all the money you made before then. The last six years makes more than the first 18. Less capital for longer works too, Or the same capital invested more conservatively for longer.

What would  reducing tax do?

Suppose you put $1,429 into an RRSP, ($1,000 out of pocket) and invest at 5% with no taxes due as you go, and do it for 20 years.

The FV is $1,429*(1.05)^20 = 3,791.52. having purchasing power of $2,551. Except for taxes due when you take money out. Assuming you can get it out for 30% you would have $2,654 a nice advantage (33%, about 1.4% more yield annually.) because you paid no tax along the way. You might get it out for less if your income drops, or you might pay more. It depends on your other income. Everything is connected.

People don’t spend it all at once

Income from the capital employed matters more than how much it is. At retirement, people live on cash flow not capital.

Suppose you decide to spend the income.

With no RRSP you would have 5% of $1,989 less tax at 30% = $69.60 to spend

With the RRSP you would have 5% of $3,791.52  less tax at 30% = $132.70 to spend. That’s 91% more income for exactly the same out of pocket investment.

Some people argue not to use an RRSP because as we saw in the first case, you don’t make enough extra money if you cash it in. You should know how you want to use it. If it is spending, then it works better. If you might want a M series BMW at retirement other ways might be better. A TFSA would likely work for you.

The Takeaway

Life has to balance. You will need money to spend when you retire or for children’s education. If you can do the arithmetic, you can see what factors matter most and which ones you can influence.

Small advantages over long times matter.

Know about investment containers that could be appropriate for you, and use them when they fit.

It is not as hard as you think, but you can’t rely on advertising. They are advertising because it benefits them.

There are formulae that relate to a series of investments. If you would like to have them email me.

You can’t do the arithmetic in you head, but a spreadsheet will do it readily. If you don’t have one, you can do it online with a Google app.

It is too important to avoid, so don’t.


I help people have more retirement income and larger, more liquid estates.

Call in Canada 705-927-4770, or email don@moneyfyi.com 

One Comment on “Arithmetic Helps Solve Retirement Planning

  1. I will be reviewing this article with J & A. Thanks Don. Jaymes

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