Question

please answer the question correct:

Explain what the Rule of 72 is. How can we use this when investing? Hint: assume U.S. long term average annual return on stocks is approx. 10%, and on long term bonds 5%. How long will it take to double your money in Stocks? Bonds? A 50/50 mix of both? What is the mathematically correct version of the Rule of 72? Why the difference?

Answer 1

FV = PV ( 1+r)ⁿ

If Invested in Stock:

FV = PV ( 1+r)ⁿ

2 = 1 ( 1 + 0.10 )ⁿ

( 1 + 0.10 )ⁿ = 2 / 1 i.e 2

(1.10)ⁿ = 2

Take Log on both sides

n Log (1.10) = Log 2

n * 0.0414 = 0.3010

n = 7.27 Years

If Invested in Bond:

FV = PV ( 1+r)ⁿ

2 = 1 ( 1 + 0.05 )ⁿ

( 1 + 0.05 )ⁿ = 2 / 1 i.e 2

(1.05)ⁿ = 2

Take Log on both sides

n Log (1.05) = Log 2

n * 0.0212 = 0.3010

n = 14.20 Years

If Invested in 50% in Bond & 50% in Equity:

FV = PV ( 1+r)ⁿ

2 = 1 ( 1 + 0.075 )ⁿ

( 1 + 0.075 )ⁿ = 2 / 1 i.e 2

(1.075)ⁿ = 2

Take Log on both sides

n Log (1.075) = Log 2

n * 0.0314 = 0.3010

n = 9.59 Years

Acc to Rule 72:

No. of Years to double = 72 / Int rate

Stock = 72 / 10 = 7.2 Years

Bond = 72 / 5 = 14.4 Years

STock & Bond = 72 / 7.5 = 9.6 Years