A sum of money doubles at compound interest in 6 years. In how many years will it become 16 times?
24 years
Under compound interest a sum grows by a fixed multiplying factor over each equal period. We are told the money doubles in 6 years, so in every 6-year block the amount is multiplied by 2.
To become 16 times the original, note that 16 = 2 × 2 × 2 × 2 = 2 to the power 4. Each factor of 2 needs one doubling period of 6 years, and four such factors are required.
Time = 4 × 6 = 24 years.
Check: after 6 years → 2 times; after 12 years → 4 times; after 18 years → 8 times; after 24 years → 16 times. This confirms 24 years.
The answer 16 years wrongly treats the number of times (16) as if it were the number of years. 48 years corresponds to 2 to the power 8 = 256 times, far too long. 96 years is longer still and is unrelated to reaching 16 times. Only 24 years gives exactly 16 times.
Correct answer: 24 years
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Important Questions from Compound Interest
- A sum of money triples itself at a certain rate of compound interest in 11 years. In how many years will it amount to 27 times of itself?
A sum of ₹10,000 amounts to ₹12,321 in 2 years at a certain rate of interest per annum, compounded annually. The rate of interest per annum is:
- If the interest earned during the 2nd year on a certain sum is ₹2,352, and the rate of interest is 5% per annum compounded annually, then the sum is:
- A sum of money triples itself at a certain rate of compound interest in 17 years. In how many years will it amount to 81 times of itself?
If the interest earned during the $2^{nd}$ year on a certain sum is ₹3,342, and the rate of interest is 20% per annum compounded annually, then the sum is:
