Question

Mr. Thomas has a 4 years cumulative time deposit account in Corporation Bank and deposits ₹ 650 per month. If he receives ₹ 36296 at the time of maturity, find:

1. the total interest earned by Mr. Thomas.
2. the rate of interest per annum.

Answer 1

Given:

Monthly deposit (P) = ₹ 650

Period = 4 years = 48 months (n = 48)

Maturity amount (MV) = ₹ 36,296

Step-wise calculation:

1. Total sum deposited = P × n

= 650 × 48

= ₹ 31,200

2. Total interest earned = MV – Total deposits

= 36,296 – 31,200

= ₹ 5,096

3. For a cumulative (recurring) deposit with simple interest, the interest on the whole deposit is

`I = P × (n(n + 1))/(2 × 12) × r/100`

4. Substitute I = 5,096, P = 650, n = 48:

`5,096 = 650 × (48 × 49)/ (2 × 12) × r/100`

48 × 49 = 2,352 and 2 × 12 = 24

So, `(2,352)/24 = 98`. 

Hence, `5,096 = 650 × 98 × r/100`

= `63,700 × r/100` 

⇒ `5,096 = (63,700r)/100`

⇒ 5,096 = 637r 

⇒ `r = (5,096)/(637)` 

⇒ r = 8 

So, r = 8% per annum.

5. Check: principal + interest = 31,200 + 5,096

= 36,296 (matches MV).