Ankita started paying ₹400 per month in a 3 years recurring deposit. After six months her brother Anshul started paying ₹500 per month in a 2½ years recurring deposit. The bank paid 10% p.a. simple interest for both. At maturity who will get more money and by how much?

For Ankita,
P = money deposited per month = ₹400,
n = number of months for which the money is deposited = 3 x 12 = 36,
r = simple interest rate percent per annum = 10

Using the formula:

$I = P \times \dfrac{n(n+1)}{2 \times 12} \times \dfrac{r}{100} \text{, we get} \\[0.7em] I = \Big( 400 \times \dfrac{36 \times 37}{2 \times 12} \times \dfrac{10}{100} \Big) \\[0.5em] \enspace\medspace = \text{₹2220}$

Using the formula:

$MV = P \times n + I \text{, we get} \ MV = (400 \times 36) + 2220 \ \qquad\medspace = 14400 + 2220 \ \qquad\medspace = \text{₹16620}$

The amount Ankita will get at the time of maturity = ₹16620.

For Anshul,
P = money deposited per month = ₹500,
n = number of months for which the money is deposited = 2 x 12 + 6 = 30,
r = simple interest rate percent per annum = 10

Using the formula:

$I = P \times \dfrac{n(n+1)}{2 \times 12} \times \dfrac{r}{100} \text{, we get} \\[0.7em] I = \Big( 500 \times \dfrac{30 \times 31}{2 \times 12} \times \dfrac{10}{100} \Big) \\[0.5em] \enspace\medspace = \text{₹1937.50}$

Using the formula:

$MV = P \times n + I \text{, we get} \ MV = (500 \times 30) + 1937.50 \ \qquad\medspace = 15000 + 1937.50 \ \qquad\medspace = \text{₹16937.50}$

The amount Anshul will get at the time of maturity = ₹16937.50.

Difference in maturity amount = 16937.50 - 16620 = 317.50

∴ Anshul will get ₹317.50 more than Ankita at maturity.