Mr. Lalit invested ₹5000 at a certain rate of interest, compounded annually for two years. At the end of first year it amounts to ₹5325. Calculate :

(i) the rate of interest.

(ii) the amount at the end of second year, to the nearest rupee.

(i) Let the rate of interest be R.

Given, amount at the end of first year = ₹5325.

Interest = Amount - Principal = ₹5325 - ₹5000 = ₹325.

Interest = $\dfrac{P \times R \times T}{100}$

$\Rightarrow 325 = \dfrac{5000 \times R \times 1}{100} \\[1em] \Rightarrow 325 = 50R \\[1em] \Rightarrow R = \dfrac{325}{50} \\[1em] \Rightarrow R = 6.5\%.$

Hence, the rate of interest is 6.5% per annum.

(ii) Amount after first year = ₹5325.

Interest for second year = $\dfrac{5325 \times 6.5 \times 1}{100} = \dfrac{34612.5}{100}$ = ₹346.125.

Amount at the end of second year = ₹5325 + ₹346.125 = ₹5671.125.

Hence, the amount at the end of second year to the nearest rupee = ₹5671.