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 person borrowed Rs. 10000 on compound interest at the rate of 40 percent per annum. If the interest is compounded half yearly, then what will be the amount to be paid after 1.5 years?
A sum of Rs. 9500 amounts to Rs. 11495 in 2 years at a certain rate percent per annum, interest compounded yearly. What is the simple interest (in Rs. ) on the same sum for the same time and double the rate?
The difference between the compound interest (compounding annually) and the simple interest on a sum of money at the rate of 40 per cent per annum for 2 years is Rs. 2400. What is the amount?
In how many years will a sum of Rs.1875 amount to Rs.2187 at 8 percent p.a. compound interest?
There is a 75 percent increase in an amount in 12.5 years at simple interest. What will be the compound interest of Rs.20000 after 3 years at the same rate?
