Question

A sum of money is invested at C.I. payable annually. The amounts of interest in two successive years are ₹ 960 and ₹ 1036.80. Find the rate of interest.

Answer 1

Given:

• Interest in first year = ₹ 960
• Interest in second year = ₹ 1036.80
• Amount is invested at compound interest (C.I.) payable annually.
• We need to find the rate of interest (r %).

Step-wise calculation:

1. Let the principal at the start of the first year be (P).

2. Interest for first year = `P xx r/100 = 960`

⇒ `P xx r/100 = 960`

⇒ `P = (960 xx 100)/r`

⇒ `P = 96000/r`

3. Principal at the start of the second year:

P + Interest of first year

= P + 960

= `96000/r + 960`

But it is simpler to express in terms of (P):

`P xx (1 + r/100)` = new principal for second year

4. Interest for the second year

= `(P xx (1 + r/100)) xx r/100`

= 1036.80

Substitute `P = 96000/r`:

`96000/r xx (1 + r/100) xx r/100 = 1036.80`

5. Simplify the above equation:

`96000/r xx ((100 + r)/100) xx r/100 = 1036.80`

Cancel (r) from numerator and denominator:

`96000 xx (100 + r)/100 xx 1/100 = 1036.80`

`96000 xx (100 + r)/10000 = 1036.80`

Multiply both sides by 10000:

96000 × (100 + r) = 1036.80 × 10000

96000 × (100 + r) = 10368000

6. Divide both sides by 96000:

`100 + r = 10368000/96000`

100 + r = 108

7. Solving for (r):

100 + r = 108

⇒ r = 8