A sum of money at compound interest doubles itself in 5 years. In how many years, it would amount to 8 times of itself at same rate of interest?
Ans. 15 Years
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Sum on maturity after n year compound interest of r% :
S = P (1 + r/100)ⁿ
2P = P (1 + r/100)⁵
(1 + r/100)⁵ = 2 ---- (1)
Sum on maturity becomes 8 times after n years at the same rate r%:
8 P = P (1 + r/100)ⁿ
8 = (1 + r/100)ⁿ --- (2)
If we cube equation (1), then we get equation (2).
So [ (1+ r/100)⁵ ]³ = 2³ = 8
So the duration is 5 * 3 = 15 years
S = P (1 + r/100)ⁿ
2P = P (1 + r/100)⁵
(1 + r/100)⁵ = 2 ---- (1)
Sum on maturity becomes 8 times after n years at the same rate r%:
8 P = P (1 + r/100)ⁿ
8 = (1 + r/100)ⁿ --- (2)
If we cube equation (1), then we get equation (2).
So [ (1+ r/100)⁵ ]³ = 2³ = 8
So the duration is 5 * 3 = 15 years
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