The simple interest on a sum of money for 2 years at 12% per annum is ₹1380. Find :

(i) the sum of money.

(ii) the compound interest on this sum for one year payable half-yearly at the same rate.

Given, S.I. = ₹1380, rate = 12% p.a. and time = 2 years.

(i) Let the sum of money be P, then

$S.I. = \dfrac{P \times R \times T}{100} \\[1em] \Rightarrow 1380 = \dfrac{P \times 12 \times 2}{100} \\[1em] \Rightarrow 138000 = 24P \\[1em] \Rightarrow P = \dfrac{138000}{24} \\[1em] \Rightarrow P = 5750.$

Hence, the sum of money is ₹5750.

(ii) Since, the rate of interest is 12% per annum, therefore, the rate of interest half-yearly = 6%.

Principal for first half-year = ₹5750.

Interest for first half-year = ₹ $\dfrac{5750 \times 6 \times 1}{100} = \dfrac{34500}{100}$ = ₹345.

∴ Amount after first half-year = ₹5750 + ₹345 = ₹6095.

Principal for the second half-year = ₹6095.

Interest for the 2nd half-year = ₹ $\dfrac{6095 \times 6 \times 1}{100} = \dfrac{36570}{100}$ = ₹365.70

∴ Compound interest on the above sum for one year payable half-yearly = ₹345 + ₹365.70 = ₹710.70

Hence, the compound interest on ₹5750 for one year payable half-yearly at the same rate is ₹710.70