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If a sum of money doubles itself in 10 years on compound interest, then in how many more years will it become 16 times of itself at the same rate of interest?
10
20
30
40
40
If a sum becomes 2k times in T years, it becomes 2n times in n├ЧT years. Since 16=24, the total time is 4├Ч10=40 years. Since the question asks for 'more' years, calculate 40тИТ10=30 years.
A sum of money doubles in 10 years at compound interest. We need to find how many 'more' years it takes to become 16 times the original sum.
A=P(1+100rтАЛ)n
If a sum becomes 2k times in T years, it becomes 2n times in n├ЧT years. Since 16=24, the total time is 4├Ч10=40 years. Since the question asks for 'more' years, calculate 40тИТ10=30 years.
Students often answer 40 instead of 30, forgetting the question asks for 'how many more' years beyond the initial 10 years.
Analyze the growth factor
The sum doubles (21) in 10 years. To reach 16 times, we express 16 as a power of 2: 16=24.
24=16
Calculate total time
In compound interest, the time required to grow by a factor of xn is n times the time required to grow by a factor of x. Total time = 4├Ч10=40 years.
TtotalтАЛ=4├Ч10=40┬аyears
Calculate 'more' years
The question asks for additional years after the first 10 years. So, we subtract the initial 10 years from the total time.
TmoreтАЛ=40тИТ10=30┬аyears
D is correct because the total time to reach 16 times is 40 years, meaning 30 more years are required after the initial 10 years.
This concept of compounding growth is identical to half-life calculations in Physics or population growth models in Biology.
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