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If a sum of money doubles itself in 10 years on compound interest, then in how many years will it become 16 times of itself at the same rate of interest?
20
10
40
30
40
In compound interest, if a sum doubles in T years, it grows geometrically. To become 2n times the original sum, the total time required is n├ЧT years.
In compound interest, if a sum doubles in T years, it grows geometrically. To become 2n times the original sum, the total time required is n├ЧT years.
This is similar to bacterial cell division (binary fission), where a population doubles every generation; if it doubles in 10 minutes, after 4 generations (40 minutes), the population increases by a factor of 16.
Rule of Geometric Power: Total Time = (Number of Doublings) ├Ч (Doubling Time).
A=P(1+100rтАЛ)t тАФ The general compound interest formula
TtotalтАЛ=n├ЧTdoublingтАЛ тАФ Relationship for power of doubling
Compound interest follows an exponential growth function A=P(1+100rтАЛ)n. Because the growth factor (1+100rтАЛ)T=2, raising this to the power of 4 (24=16) requires the time interval to be multiplied by 4, resulting in 4├Ч10=40 years.
Compound interest exhibits constant percentage growth, leading to exponential curves.
The time taken to reach a multiple M follows the relationship M=2n, where n is the number of doubling periods.
Exponential growth is characterized by the doubling time being independent of the initial principal.
Predictable long-term growth
Applicable to biological population models
Assumes constant interest rate over long durations
Does not account for inflation or external variables
Financial investment growth
Radioactive decay (half-life calculations)
16 is expressed as 24, indicating 4 doublings are needed.
Wrong options explanation: Option A assumes linear addition instead of geometric multiplication; Option B is the base interval; Option D underestimates the growth cycle.
C is correct тАФ The sum follows geometric progression where 24=16, requiring 4 cycles of 10 years each to equal 40 years.
Always convert target multiples into powers of the base growth factor (e.g., 16 to 24) to quickly solve exponential growth problems in both finance and physics (half-life).
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