Govind borrows ₹ 18000 at 10% simple interest. He immediately invests the money at 10% compound interest compounded half-yearly. How much money does Govind gain in one year ?

Calculating simple interest :

P = ₹ 18000

R = 10%

T = 1 year

I = $\dfrac{P \times R \times T}{100} = \dfrac{18000 \times 10 \times 1}{100}$ = 1800.

Amount Govind needs to return = P + I = ₹ 18000 + ₹ 1800 = ₹ 19800.

Calculating compound interest :

For 1st half year :

P = ₹ 18000

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

R = 10%

I = $\dfrac{P \times R \times T}{100} = \dfrac{18000 \times 10 \times \dfrac{1}{2}}{100}$ = 900.

Amount = P + I = ₹ 18000 + ₹ 900 = ₹ 18900.

For 2nd half-year :

P = ₹ 18900

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

R = 10%

I = $\dfrac{P \times R \times T}{100} = \dfrac{18900 \times 10 \times \dfrac{1}{2}}{100}$ = 945.

Amount Govind will get back = P + I = ₹ 18900 + ₹ 945 = ₹ 19845.

Gain = Amount Govind will get back - Amount Govind will return

= ₹ 19845 - ₹ 19800 = ₹ 45.

Hence, Govind will gain ₹ 45 in one year.