# A Sum Of Money Invested At 8% Per Annum For Simple Interest Amounts To Rs 12122 In 2 Years. What Will It Amounts To In 2 Year 8 Months At 9% Rate Of Interest?

Given:

Amount = Rs 12122

Time period, t = 2 years

Rate of interest, r = 8%

Amount = Principal + Interest

$$\Rightarrow 12122 = P + \frac{PTR}{100}$$ $$\Rightarrow 12122 = \frac{100P + PTR}{100}$$ $$\Rightarrow 12122 = \frac{P(100 + TR)}{100}$$ $$\Rightarrow 12122 = \frac{P(100 + 2 * 8)}{100}$$ $$\Rightarrow 12122 = \frac{P(100 + 16)}{100}$$ $$\Rightarrow P = \frac{P116}{100}$$ $$\Rightarrow P = 12122 * \frac{100}{116}$$

Therefore,Principal (P) = Rs 10450.

Amount in two years eight months (32 months) and the rate of interest, r = 9% per annum.

Amount = Principal + Interest

$$\Rightarrow A = P + \frac{PTR}{100}$$

Since two years eight months (32 months) =$$\frac{8}{3} years$$ $$\Rightarrow A = 10450 + \frac{10450 * \frac{8}{3} * 9}{100}$$ $$\Rightarrow A = 10450 + \frac{250800}{100}$$ $$\Rightarrow A = 10450 + 2508$$ $$\Rightarrow A = 12958$$

Therefore, Amount, A = Rs.12958

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