Anwesha intended to open a Recurring Deposit account of ₹ 1000 per month for 1 year in a Bank, paying a 5% per annum rate of simple interest. The bank reduced the rate to 4% per annum. How much must Anwesha deposit monthly for 1 year so that her interest remains the same?

1. ₹ 12325

2. ₹ 1250

3. ₹ 1200

4. ₹ 1000

In first case :

P = ₹ 1000

r = 5%

n = 12 months

Interest = $P \times \dfrac{n(n + 1)}{2 \times 12} \times \dfrac{r}{100}$

$= 1000 \times \dfrac{12 \times (12 + 1)}{2 \times 12} \times \dfrac{5}{100} \\[1em] = 1000 \times \dfrac{12 \times 13}{2 \times 12} \times \dfrac{1}{20} \\[1em] = 25 \times 13 \\[1em] = ₹ 325.$

In second case :

P = ₹ x (Let)

r = 4%

n = 12 months

Interest = ₹ 325

$\therefore 325 = x \times \dfrac{12 \times 13}{2 \times 12} \times \dfrac{4}{100} \\[1em] \Rightarrow 325 = x \times \dfrac{13}{2} \times \dfrac{1}{25}\\[1em] \Rightarrow x = \dfrac{325 \times 25 \times 2}{13} \\[1em] \Rightarrow x = \dfrac{16250}{13} = \text{₹ 1250.}$

Hence, Option 2 is the correct option.