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A sum of money becomes Rs2,000 in 3 years and Rs2,400 in 4 years, at the certain rate of yearly compound interest in case of
annual compounding. Find the yearly rate of compound interest.
20%
10%
15%
25%
To determine the yearly rate of compound interest, consider the given information:
- The amount grows from Rs2,000 in 3 years to Rs2,400 in 4 years.
- In 1 year, the amount increases by Rs400 (Rs2,400 - Rs2,000).
Now, let's find the rate:
- Initial Amount at the end of 3 years: Rs2,000
- Amount after 4 years: Rs2,400
- The formula for compound interest for 1 year can be written as:
$$
A = P \times (1 + r)^n
where A is the amount after 4 years, P is the amount after 3 years, r is the rate, and n is 1 year.
- Calculation:
2400 = 2000 \times (1 + r)
1 + r = \frac{2400}{2000} = 1.2
- Solving for r:
r = 1.2 - 1 = 0.2
- Convert to percentage:
r = 20\%
- Correct Option:
- Option 1: 20%
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