A sum under compound interest triples in 3 years. In how many years will it increase to 9 times its original value?
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Answer: D. 6
Explanation
Compound interest causes financial sums to grow geometrically over regular fixed time interval periods. If a sum triples every three years, tripling it again multiplies the original principal by nine total times. Multiplying the required tripling cycles by the three-year period duration gives a total time of six years. Compound interest formulas calculate exponential growth where interest earns additional interest over time intervals. Geometric progression principles govern the growth of investments under fixed compound interest rate conditions. Exponential time scaling means doubling the growth factor requires doubling the elapsed time duration.
Financial planners calculate long-term investment growth horizons using compound interest doubling and tripling rules. Biologists model bacterial population expansion rates using exponential geometric growth time interval formulas. Economists project sovereign debt accumulation over multi-year periods using compound growth rate projections. Option A suggests eighteen years which overestimates the time required for exponential compound growth. Option B suggests twelve years which assumes linear rather than geometric compound growth rates. Option C suggests nine years which miscalculates the required number of compounding tripling periods.
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