Question

a. If the interest rate is 7.0% per year, approximately how long will it take for your money to quadruple in value? (Use the Rule of 72.)

b. If the inflation rate is 4.5% per year, what will be the change in the purchasing power of your money over this period? (Use the Rule of 72 to compute the number of years. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Answer 1

Solution:-

(a) As per rule 72, the number of years required to double the money on an investment are calculated as follows:

Number of years= 72 / Interest rate

In the given question, the interest rate is 7%, therefore number of years required to double the money is as follows:

No. of years to double= 72/7= 10.286 years

Now, to quadruple the money, the investor will have to again double the money twice. Therefore, the number of years required to quadruple the investment is as follows:

No. of years to quadruple= 10.286 years*2= 20.57 years

(b) The question requires us to calculate the change in purchasing power in the calculated period of 20.6 years if the inflation rate is 4.5% annually

Let's say that the initial investment is $100. So, how much money after 20.57 years will have the same purchasing power that $100 has today? Let's calculate that value as follows:

Inflation-adjusted value of $100 after 20.57 years= $100*(1+4.5%)^20.57

Inflation-adjusted value= $247.36

Now, the value of our investment after the said 20.57 years will the quadrupled figure of $400 (i.e. $100*4).

Therefore, the change in purchasing power of money over this period is calculated as follows:

Change in purchasing power (%)= ($400-$247.36)/($247.36)

Change in purchasing power (%)= 61.71%