Question

Mr. Aggarwal has a cumulative deposit account of ₹ 400 per month at 10% per annum simple interest. If he gets ₹ 30100 at the time of maturity, find the total time for which the account was held.

Answer 1

Given:

Monthly deposit, P = ₹ 400

Rate of interest, r = 10% per annum

Maturity Value (MV) = ₹ 30100

Time = n months

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

Let’s simplify the equation:

`30100 = 400n + (400xxn(n+1)xx10)/2400`

`=> 30100 = 400n+(4000xxn(n+1))/2400`

`=> 30100=400n+(5n(n+1))/3`

Multiply entire equation by 3 to eliminate denominator:

3 ⋅ 30100 = 1200n + 5n(n + 1)

⇒ 90300 = 1200n + 5n2 + 5n

⇒ 5n² + 1205n − 90300 = 0

n² + 241n − 18060 = 0

`n = (-241 +- sqrt(241^2+4xx18060))/2`

`n = (-241 +- sqrt(58081+72240))/2`

`n = (-241 +- sqrt(130321))/2`

`= (-241 +-361)/2`

`n = 120/2`

= 60

n = 60 months

= 5 years