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Question
Nikita invests Rs. 6000 for two years at a certain rate of interest compounded annually. At the end of the first year, it amounts to Rs. 6720. Calculate:
- the rate of interest.
- the amount at the end of the second year.
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Solution
Given: P = Rs. 6000,
A = Rs. 6720
n = 1 year
Formula: `A = P(1 + r/100)^n`
1) Substituting values we get:
⇒ 6720 = `6000(1 + r/100)^1`
⇒ `6720/6000 = 1 + r/100`
⇒ `6720/6000 - 1 = r/100`
⇒ `(6720 - 6000)/6000 = r/100`
⇒ `720/6000 = r/100`
⇒ `r = (720 xx 100)/6000`
⇒ r = 12%
2) `A = P(1 + r/100)^n`
`⇒ A = 6000 xx (1 + 12/100)^2`
`⇒ A = 6000 xx ((100 + 12)/100)^2`
`⇒ A = 6000 xx ((112)/100)^2`
`⇒ A = 6000 xx (28/25)^2`
`⇒ A = 6000 xx 784/625`
⇒ A = 7526.40
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