The rule of 72 is a rule of thumb for finding how long it takes money at interes
ID: 2728017 • Letter: T
Question
The rule of 72 is a rule of thumb for finding how long it takes money at interest to double: If r is the annual interest rate, then the doubling time is approximately 72/(100r) years. (a) Calculate the balance at the end of the predicted doubling time for each $1000, with annual compounding, for the small growth rates of 3%, 4%, and 6% (b) Repeat part (a) for the intermediate interest rates of 8% and 9%. (c) Repeat part (a) for the larger interest rates of 12%, 24%, and 36%. (d) What do you conclude about the rule of 72?
Explanation / Answer
(a)
Future value (F) = Present value (1 + rate of interest)Time in years
F = P (1 + R)T
Dividing both the sides by P.
F/P = (1 + R)T
If the present value doubles , then F/P = 2
2 = (1 + R)T
Taking log both the sides,
In (2) = In (1+R)T
In (2) = T * In (1 + R) [ Log ab = b* Log a]
When Rate on interest = 3%, T = In (2) / In (1 + 0.03) = In (2) / In (1.03) , by solving we will get T = 23.45 .
When Rate on interest = 4%, T = In (2) / In (1 + 0.04) = In (2) / In (1.04) , by solving we will get T = 17.67 .
When Rate on interest = 6%, T = In (2) / In (1 + 0.06) = In (2) / In (1.06) , by solving we will get T = 11.90 .
By using rule of 72:-
when r = 3 %, T = 72/3 = 24
when r = 4 %, T = 72/4 = 18
when r = 6 %, T = 72/6 = 12
Conclusion:- The rule of 72 is very very nearest to the actual calculation.
b)
When Rate on interest = 8%, T = In (2) / In (1 + 0.08) = In (2) / In (1.08) , by solving we will get T = 9 .
When Rate on interest = 9%, T = In (2) / In (1 + 0.09) = In (2) / In (1.09) , by solving we will get T = 8.04
By using rule of 72:-
when r = 8 %, T = 72/8 = 9
when r = 9 %, T = 72/9 = 8
Conclusion:- The rule of 72 is very very nearest to the actual calculation.
d) Conclusion about Rule 72:- The thumb rule of 72 estimate the number of years required to double your money at a given annual rate of return in the question.
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