Question

The maturity value of a R.D. Account is ₹ 3,320. If the monthly instalment is ₹ 400 and the rate of interest is 10%; find the time (period) of this R.D. Account.

Answer 1

Maturity value = ₹ 3,320

Instalment per month (P) = ₹ 400

Number of months (n) = n

Let rate of interest (r) = 10% p.a.

∴ `S.I. = P xx (n(n + 1))/(2 xx 12) xx r/100`

The Maturity Value (MV) is the sum of all monthly deposits plus the interest earned:

MV = (P × n) + I

3,320 = `(400 xx n) + (400 xx (n(n + 1))/24 xx 10/100)`

Simplify the interest term:

3,320 = `400n + (400 xx (n(n + 1))/240)`

3,320 = `400n + (40n(n + 1))/24`

3,320 = `400n + (5n(n + 1))/3`

Multiply by 3:

3,320 × 3 = (400n × 3) + 5n(n + 1)

9,960 = 1200n + 5n² + 5n

5n² + 1205n − 9960 = 0

Divide the whole equation by 5 to simplify:

n² + 241n − 1992 = 0

Solving the quadratic equation

n² + 249n − 8n − 1,992 = 0

n(n + 249) − 8(n + 249) = 0

(n − 8)(n + 249) = 0

n = 8 or n = −249

Since time (number of months) cannot be negative,

n = 8 months

The time period of the Recurring Deposit account is 8 months.