# A sum invested at 10% per annum amounts to Rs. 20,947.50 at the end of one year, when the interest is compounded half-yearly. What will be the simple

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A sum invested at 10% per annum amounts to Rs. 20,947.50 at the end of one year, when the interest is compounded half-yearly. What will be the simple interest (in Rs.) on the same sum for $4\frac{2}{5}$ years at triple the earlier rate of interest?
1. 25,080
2. 42,020
3. 26,500
4. 27,000

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Correct Answer - Option 1 : 25,080

Given:

A sum invested at 10% per annum amounts to Rs. 20,947.50 in one year, interest is compounded half-yearly

Formula used:

Simple Interest = (P × r × t)/100

Compound interest

⇒ A = P × {1 + (r/100)}t

Where P = Principal

A = Amount

r = Rate of Interest

t = Time

Calculation:

The rate of interest is 10% per annum

But the interest is compounded half-yearly

So, rate of interest will become 10/2 = 5%

⇒ 20947.50 = P × {1 + (5/100)}2

⇒ 20947.50 = P × (21/20)2

⇒ P = 20947.50 × (20/21)2

⇒ P = 19000

According to the question, the rate of interest is tripled.

⇒ r = 10 × 3 = 30%

The simple interest for 22/5 years is

⇒ {19000 × 30 × (22/5)}/100

⇒ (19000 × 6 × 22)/100

⇒ 2508000/100 = Rs. 25080

∴ The simple interest for $4\frac{2}{5}$ is Rs. 25080.