Compounding and the Time Value of Money

Compounding and the Time Value of Money

The two most important factors in building wealth

A higher return on investment greatly increases your wealth

Even moderate increases in return greatly increase your wealth

Why you should invest a healthy amount of your savings in stocks

The rule of 72

How to price any security or property using discounted cash flow

The two most important factors in building wealth

The the return on investment

The amount of time in the investment

A higher return on investment greatly increases your wealth

Increasing your return on investment greatly increases your wealth over long periods of time

You might think that increasing your return from the typical bond rate of 5 percent to the typical stock rate of 10 percent might, at most, double your money with stocks relative to bonds

But after 30 years, the amount invested in stocks is worth four times as much as the amount invested in bonds

Num years in investment	Invest in 5% bonds	Invest in 10% stocks	Ratio stock / bond value
0	$100	$100	1.0
1	105	110	1.0
2	110	121	1.1
3	116	133	1.1
4	122	146	1.2
5	128	161	1.3
...	...	...	...
10	163	259	1.6
...	...	...	...
15	208	418	2.0
...	...	...	...
20	265	673	2.5
...	...	...	...
30	432	1,745	4.0
...	...	...	...
40	704	4,526	6.4

Even moderate increases in return greatly increase your wealth

Don't scoff at slight increases in return

Even increasing your return from 5 percent in bonds to 7 percent (achieved through a blend of stocks and bonds) gives you 50 percent more money after 20 years

Num years in investment	Invest in 5% bonds	Invest in 7% blend	Ratio blend / bond value
0	$100	$100	1.0
1	105	107	1.0
2	110	114	1.0
3	116	123	1.1
4	122	131	1.1
5	128	140	1.1
...	...	...	...
10	163	197	1.2
...	...	...	...
20	265	387	1.5
...	...	...	...
30	432	761	1.8
...	...	...	...
40	704	1,497	2.1

Investing early is critical

The twin sister case

Sister A saves $2,000 each year from age 25 to 34 for a total of $10,000 saved

Sister A then stops saving entirely

Sister B saves $2,000 each year from age 35 to 64 for a total of $60,000 saved

Sister saves more in total, but starts later than A

Both sisters invest in identical stock mutual funds that return 10 percent annually

At age 65, the early saver has almost twice as much money as her late-starting sister, eventhough the late starter saved six times more money

Age	Sister A's ann savings	Sister A's total savings	Sister B's ann savings	Sister B's total savings
25	$2,000	$2,000	$0	$0
26	2,000	4,200	0	0
...	...	...	...	...
33	2,000	27,159	0	0
34	2,000	31,875	0	0
35	0	35,062	2,000	2,000
36	0	38,569	2,000	4,200
...	...	...	...	...
50	0	146,464	2,000	71,899
...	...	...	...	...
63	0	505,634	2,000	297,262
64	0	556,197	2,000	328,988
65	0	611,817	0	361,887
66	0	672,998	0	398,076

Why you should invest a healthy amount of your savings in stocks

Long-term average returns on various assets

Asset	Return
Inflation	3%
Money market funds	3.5
Long-term bonds	5.5
Stocks	10

After taxes and inflation, only stocks have provided a positive return

The rule of 72

To see how long it will take for your investment to double in value, divide 72 by your expected return on investment

Example

Time required at various inflation rates for prices to double

Inflation rate	Years required for prices to double
2%	36
3	24
4	18
5	14
6	12

With moderate inflation of 5 percent, prices can double in 14 years

Since you may be in retirement for 15 years or more, will your income double during this time to keep up with inflation?

How to price any security or property using discounted cash flows

All stocks and bonds can be priced using discounted cash flows

A dollar you receive one year from now is not worth a dollar today

Today's value depends on prevailing interest rates

If interest rates are 5 percent, the future dollar is worth 95.2 cents today

If interest rates are 10 percent, the future dollar is worth 90.9 cents today

Depends on the risk associated with receiving that dollar in the future

The above examples assumed you were guaranteed of getting the dollar in the future

If the investment involves risk, the future dollar may be worth only 70 cents today