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# A sum of money invested at 8% per annum for simple interest amounts to Rs.12,122 in 2 years. What will it amount to in 2 year 8 months at 9% rate of interest?

**Given:** A sum of money invested at 8% per annum for simple interest amounts to Rs.12,122 in 2 years.

**To find: ** What will it amount to in 2 year 8 months at 9% rate of interest.

**Solution:**

Let the principal = P Rate, R = 8% SI; T = 2 years

Amount = Rs12,122

Simple interest SI = $\frac{PTR}{100}$ = $\frac{P\times2\times8}{100} = \frac{4P}{25}$

Amount = P + SI = P + $\frac{4P}{25} $= $\frac{25P + 4P}{25} = \frac{29P}{25} = 12122$

P = $12122 \times \frac{25}{29} = 10,450$

T = 2 yr 8 months = 2 $\frac{8}{12} = 2 \frac{2}{3}$ = $\frac{8}{3}$ yrs; Rate R = 9%

SI =$\frac{PTR}{100}$ = $\frac{10,450 \times \frac{8}{3} \times 9}{100} = 2508$

**Amount at the end of 2 years 8 months = P + SI = 10,450 + 2508**

** = Rs 12,958**

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