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Question
Nikita invests Rs.6,000 for two years at a certain rate of interest compounded annually. At the end of first year it amounts to Rs.6,720. Calculate:
(a) The rate of interest.
(b) The amount at the end of the second year.
Solution
Let X % be the rate of interest.
P = Rs. 6,000, n = 2 years, A = Rs.6,720
For the first year
A = P`( 1 + r/100)^n`
⇒ 6,720 = 6,000`( 1 + "X"/100 )^1`
⇒ 6,720 - 6,000 = 60X
⇒ X = 12
The rate of interest is X % = 12 %.
The amount at the end of the second year.
A = P`( 1 + r/100)^n`
⇒ A = 6,000`( 1 + 12/100 )^2`
⇒ A = 6,000`( 112/100 )^2`
⇒ A = 7,526.40
The amount at the end of the second year = Rs. 7,526.40
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