Question

Double your wealth. Kant Miss Company is promising its investors that it will double their money every 3 years. What annual rate is Kant Miss​ promising? Is this investment a good​ deal? If you invest ​$200 now and Kant Miss is able to deliver on its​ promise, how long will it take your investment to reach ​$30,000​?

Using the Rule of​ 72, what annual rate is Kant Miss​ promising?

Years?

Answer 1

Formula for compound interest can be used to compute interest rate as:

A = P x (1 + r/m) ⁿ

P = Principal

A = Future value of investment = 2 x P

r = Rate of interest

m = No. of compounding in a year = 1 (Assumed)

n = No. of periods = 3

2P = P x (1+r) ³

2P / P = (1+r) ³

(1+r) ³ = 2

1+r = 2 ^1/3

1+r = 2 ^0.333333333

1 + r = 1.25992104989

r = 1.25992104989 – 1 = 0.25992104989 or 25.99 %

Kant Miss Company is promising 25.99 % annual rate.

Again the above equation can be used to compute number of period n.

P = $ 200, A = $ 30,000, r = 25.99 %

$ 30,000 = $ 200 x (1+0.2599) ⁿ

$ 30,000 = $ 200 x (1.2599) ⁿ

(1.2599) ⁿ = $ 30,000 / $ 200

(1.2599) ⁿ = 150

Taking logarithm of both sides and solving we get, n as:

n x log 1.2599 = 150

n x 0.10033607593 = 2.17609125906

n = 2.17609125906/0.10033607593 = 21.68802436 or 22 years

It will take 22 years to reach the investment to $ 30,000.

As per rule 72:

72/annual return = Number of periods to double the investment.

We can re-write the equation as:

Annual return = 72/ Number of periods to double the investment

                       = 72/3 = 24 or 24 %

Annual rate, Kant Miss​Company promising is computed to be 24 % using rule 72