Geeta borrowed ₹ 15000 for 18 months at a certain rate of interest compounded semi-annually. If at the end of six months it amounted to ₹ 15600; calculate :

(i) the rate of interest per annum.

(ii) the total amount of money that Geeta must pay at the end of 18 months in order to clear the account.

(i) Difference between C.I. of two successive half-years = ₹ 15600 - ₹ 15000 = ₹ 600

∴ ₹ 600 is the interest of $\dfrac{1}{2}$ year on ₹ 15000.

By formula,

Rate of interest = $\dfrac{100 \times I}{P \times T} = \dfrac{100 \times 600}{15000 \times \dfrac{1}{2}} = \dfrac{120}{15}$ = 8%

Hence, the rate of interest = 8%.

(ii) For 2nd half-year :

P = ₹ 15600

T = $\dfrac{1}{2}$ year

R = 8%

I = $\dfrac{P \times R \times T}{100} = \dfrac{15600 \times 8 \times \dfrac{1}{2}}{100}$ = ₹ 624.

Amount = P + I = ₹ 15600 + ₹ 624 = ₹ 16224.

For 3rd half-year :

P = ₹ 16224

T = $\dfrac{1}{2}$ year

R = 8%

I = $\dfrac{P \times R \times T}{100} = \dfrac{16224 \times 8 \times \dfrac{1}{2}}{100}$ = ₹ 648.96

Amount = P + I = ₹ 16224 + ₹ 648.96 = ₹ 16872.96

Hence, amount needed to pay at the end of 18 months = ₹ 16872.96