Question

ASSIGNMENT 1 1. Katie says the “Rule of 72” is a great mental math shortcut to estimate the effect of any growth rate, from quick financial calculations to population estimates. Here's the Rule of 72 formula in terms of the time value of money: (Number of compounding periods to double your money) = 72 / [Interest Rate (%)] This formula is useful for financial estimates and understanding the nature of compound interest. Use the Rule of 72 to estimate the time to: (a) Double your money at 6% per year, compounded annually (b) Double your money at 12% per year, compounded monthly (c) Double your money at 30% per year, compounded annually Now calculate the actual time for (a), (b), and (c). Is the Rule of 72 an accurate estimate?

Answer 1

a. Time to double the money = 72 / 6 = 12 yrs

b. time to double the money = 72 / 12 = 6 yrs

c. time to double the money = 72 / 30 = 2.4 yrs

F = P *( 1+i)^t

For double the money, F = 2P

a. 2 P = P *( 1+0.06)^t

1.06^t = 2

taking log both sides

t = log 2 / log 1.06 = 11.8956 yrs = 11.90 yrs

b.

2 P = P *( 1+0.12)^t

1.12^t = 2

taking log both sides

t = log 2 / log 1.12 = 6.116 yrs = 6.12 yrs

c .

2 P = P *( 1+0.3)^t

1.3^t = 2

taking log both sides

t = log 2 / log 1.3 = 2.64 yrs

Rule of 72 is approximate measure