What is the minimum number of complete years for a sum at 20% compound interest to more than double_________?
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Answer: B. 4
Explanation
At twenty percent compound interest, the investment growth multiplier each year is one point two. For three years, the multiplier is one point two cubed, equaling one point seven two eight, which is less than doubling. For four years, the multiplier is one point two to the fourth power, equaling two point zero seven three six, which successfully exceeds the double threshold. Compound interest growth is exponential, modeled by the formula principal times one plus r to the power of n. Doubling an investment means the growth multiplier must reach or exceed a value of two point zero. Evaluating integer exponents sequentially allows us to determine the exact minimum complete years required for financial goals.
Option A results in a growth factor of one point seven two eight, meaning the sum has not yet doubled. Option C exceeds the requirement but fails to represent the minimum complete number of years needed. Option D suggests a duration longer than necessary since the investment already doubles during the fourth year.
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- Mathematics
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- Mathematics
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- —
- Difficulty
- medium
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