Question

A sum of ₹ 48000 amount to ₹ 55566 in 18 months when the interest is reckoned half-yearly. Find the rate of interest per annum.

Answer 1

Given:

• Principal, (P = ₹ 48000)
• Amount after 18 months, (A = ₹ 55566)
• Time, (T = 18) months = 1.5 years
• Interest is compounded half-yearly
• Need to find the rate of interest per annum, (r%)

Step-wise calculation:

1. Since interest is compounded half-yearly, the number of half-year periods in 18 months = `18/6` = 3.

2. The formula for compound amount when interest is compounded (n) times a year:

`A = P(1 + (r//2)/100)^n` where `(r/2)` is the half-yearly rate of interest and n = 3.

3. Substitute the known values:

`55566 = 48000 xx (1 + r/200)^3`

4. Divide both sides by 48000:

`(1 + r/200)^3 = 55566/48000`

`(1 + r/200)^3 = 1.157625`

5. Take the cube root on both sides to solve for `1 + r/200`:

`1 + r/200 = root(3)(1.157625)`

6. Calculate `root(3)(1.157625)`: 

`root(3)(1.157625) ≈ 1.05`

7. So, `1 + r/200 = 1.05`

⇒ `r/200 = 0.05`

⇒ r = 0.05 × 200

⇒ r = 10

The rate of interest per annum is 10%.