Question

Tanvy has a recurring deposit account in a finance company for `1 1/2` years at 9% per annum. If she gets ₹ 15426 at the time of maturity, how much per month has been invested by her?

Answer 1

Given:

Time = `1 1/2` years = 18 months

Rate = 9% per annum (simple interest on RD)

Maturity amount (MV) = ₹ 15,426

Let monthly instalment = ₹ P

Step-wise calculation:

1. For a recurring deposit, MV = P × n + I, where I is the total simple interest on the monthly instalments.

The interest formula used for monthly instalments gives

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

2. Therefore, `MV = P xx n + P xx r/100 xx (n(n + 1))/24`

⇒ `MV = P xx [n + r xx (n(n + 1))/2400]`

3. Substitute n = 18 and r = 9:

`MV = P xx [18 + (9 xx 18 xx 19)/2400]`

= `P xx [18 + 3078/2400]`

= P × [18 + 1.2825] 

= P × 19.2825

4. Solve for P:

`P = (15,426)/(19.2825)`

P = 800

Tanvy invested ₹ 800 every month.