Mr. Narahari deposited ₹1,50,000 today at 7.5% interest rate in SBI fixed deposit. He is interested in knowing if he keeps this money in FD, after how many years his investment will get doubled? You are requested to apply (i) Rule of 69 and (ii) Rule of 72 for computational purpose.
Ms. Dejamma has invested Rs. 10,000 on the first day of the month in a mutual fund for a period of 6 months. At the time of maturity, she received a sum of Rs. 14,000 yielding a return of 80% p.a. She is interested in knowing after how many months the amount invested by her would have doubled considering all the factors in which the business operates remain unchanged as it was earlier.
Answer (1)
To determine how long it will take for an investment to double using different rules of thumb, we'll use Mr. Narahari's fixed deposit example and Ms. Dejamma's mutual fund investment.
Part 1: Mr. Narahari's Fixed Deposit
Initial Data:
Principal amount: ₹1,50,000
Interest rate: 7.5% per annum
(i) Using the Rule of 69
The Rule of 69 is a quick way to estimate the doubling time in years for an investment using continuous compounding. The formula is:
Doubling Time = Interest Rate (as a percentage) 69
Substituting the given interest rate:
Doubling Time = 7.5 69 ≈ 9.2 years
(ii) Using the Rule of 72
The Rule of 72 is another simple formula to estimate the number of years required to double an investment using compounded interest. The formula is:
Doubling Time = Interest Rate (as a percentage) 72
Substituting the given interest rate:
Doubling Time = 7.5 72 ≈ 9.6 years
Part 2: Ms. Dejamma's Mutual Fund Investment
Initial Data:
Initial Investment: Rs. 10,000
Return Amount: Rs. 14,000
Time Period: 6 months
Annual return: 80%
To find out after how many months her investment would double, considering it grows at this rate, let's calculate monthly growth first.
The effective monthly interest rate can be approximated by dividing the annual rate by 12:
Monthly Interest Rate = 12 80 ≈ 6.67%
Using the Rule of 69 with monthly compounding, the formula for doubling time in months is:
Doubling Time = Monthly Interest Rate 69
Doubling Time = 6.67 69 ≈ 10.3 months
Conclusion
For Mr. Narahari, it would take approximately 9.2 years using the Rule of 69 and 9.6 years using the Rule of 72 to double his fixed deposit.
For Ms. Dejamma, under the given conditions and using monthly compounding with the Rule of 69, the investment will double in approximately 10.3 months if the rate of return remains constant.
