Garima borrowed ₹ 40,000 at 10% p.a. simple interest. She immediately inverted this money at 10% p.a., compounded half-yearly. Calculate Garima's gain in 18 months.

For simple interest:

P = ₹ 40,000, R = 10 %, T = $\dfrac{18}{12}$ years

$\text{S.I.} = \dfrac{P \times R \times T}{100}\\[1em] = \dfrac{40,000 \times 10 \times \dfrac{18}{12}}{100}\\[1em] = \dfrac{600,000}{100}\\[1em] = 6,000$

Total amount to be paid at the end of 18 months = Borrowed amount + Interest = 40000 + 6000 = ₹ 46000

For compound interest:

P = ₹ 40,000, R = $\dfrac{10}{2}$ % = 5 %, T = $\dfrac{18}{12} \times 2$ = 3 years

A = P $\Big(1 + \dfrac{R}{100}\Big)^n$

= 40,000 x $\Big(1 + \dfrac{5}{100}\Big)^3$

= 40,000 x $(1 + 0.05)^3$

= 40,000 x $(1.05)^3$

= 40,000 x 1.157625

= 46,305

Compound Interest = Amount - Principal

= 46,305 - 40,000

= 6,305

Profit = Compound Interest - Simple Interest = ₹ 6,305 - 6,000 = ₹ 305

Hence, Garima's total gain in 18 months = ₹ 305.