Question

Amit deposited ₹ 600 per month in a recurring deposit account. The bank pays a simple interest of 12% p.a. Calculate the:

1. number of monthly instalments Amit deposits to get a maturity amount of ₹ 11826? 
2. total interest paid by the bank. 
3. total amount deposited by him.

Answer 1

Given:

Monthly instalment P = ₹ 600.

Rate r = 12% p.a. (simple interest on recurring deposit).

Maturity amount MV = ₹ 11,826.

Use recurring-deposit interest formula:

`I = P xx [(n(n + 1))/(2 xx 12)] xx (r/100)` and MV = P × n + I

Step-wise calculation:

1. Compute interest formula for these values:

`I = 600 × [(n(n + 1))/24] xx (12/100)`

Simplify: `600 × (12/100) = 72` and `72/24 = 3`

So, I = 3 × n(n + 1).

2. Maturity value:

MV = P × n + I

= 600n + 3n(n + 1)

= 3n² + 603n

3. Set MV = 11,826 and solve for n:

3n² + 603n = 11,826

⇒ Divide by 3: n² + 201n – 3,942 = 0.

4. Solve quadratic:

Discriminant D = 201² + 4 × 3

942 = 40,401 + 15,768

= 56,169

= 237²

`n = (-201 ± 237)/2` 

⇒ Positive root `n = (-201 + 237)/2`

= `36/2`

= 18 months

5. Total amount deposited

= P × n

= 600 × 18

= ₹ 10,800

6. Total interest paid

= MV – Total deposited

= 11,826 – 10,800

= ₹ 1,026