Question

Rajiv has a recurring deposit account in a bank of ₹ 600 per month. If the bank pays the interest at 7% p.a. and he gets ₹ 15450 as maturity amount, the total time period is ______.

विकल्प

• 30 months

• 36 months

• 24 months

• 42 months

Answer 1

Rajiv has a recurring deposit account in a bank of ₹ 600 per month. If the bank pays the interest at 7% p.a. and he gets ₹ 15450 as maturity amount, the total time period is 24 months.

Explanation:

Given:

Monthly deposit, P = ₹ 600

Rate of interest, r = 7% p.a.

Maturity value, MV = ₹ 15450

MV = `(Pxxn(n+1)xxr)/(2xx12xx100)`

`15450 = 600n + (600xxn(n+1)xx7)/(2400)`

`15450 = 600n+ (4200n(n+1))/2400`

`=> 15450 = 600n + (7n(n+1))/4`

61800 = 2400n + 7n(n + 1)

⇒ 61800 = 2400n + 7n² + 7n

⇒ 7n² + 2407n − 61800 = 0

Solve the quadratic equation:

n² + 343.86n − 8828.57 = 0

Total deposit = 600 ⋅ 18 = ₹ 10800

Interest

`= (600xx18xx19xx7)/2400`

`=1436400/2400`

= ₹ 598.5

MV = ₹ 10800 + ₹ 598.5 = ₹ 11398.5

Try n = 24:

Deposit = ₹ 14400

Interest

`= (600xx24xx25xx7)/2400`

`= 2520000/2400`

= ₹ 1050

MV = ₹ 15450

24 months

= 2 years