Maths · Arithmetic and Geometric progressions
A sum of money at compound interest amount to three times of its self in three y
A sum of money at compound interest amount to three times of its self in three years. in how many years will it be nine times of its self?
- A. 6 years
- B. 5 years
- C. 9 years
- D. 7 years
Step-by-step solution
Let principal be P and rate r. After 3 years, amount = 3P => P(1+r)^3 = 3P => (1+r)^3 = 3. Let t be time to become 9P: P(1+r)^t = 9P => (1+r)^t = 9 = 3^2. Since (1+r)^3 = 3, then (1+r)^t = (3)^(t/3) = 3^2 => t/3 = 2 => t = 6 years.
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