There is 80% increase in an amount in 8 years at simple interest. What will be the compound interest of Rs. 14,000 after 3 years at the same rate ?

Question

Accepted Answer

To determine the compound interest on Rs. 14,000 after 3 years at the same rate, we first need to find the rate of interest. Given that there is an 80% increase in an amount over 8 years at simple interest, we can calculate the rate of interest as follows:

1. **Calculate the Simple Interest Rate:**
   - An 80% increase over 8 years implies that the simple interest is 80% of the principal.
   - Simple Interest (SI) = Principal × Rate × Time / 100
   - 80% of Principal = Principal × Rate × 8 / 100
   - 80 = Rate × 8
   - Rate = 80 / 8 = 10%

2. **Calculate the Compound Interest:**
   - Now that we know the rate is 10%, we can calculate the compound interest for 3 years.
   - Compound Interest (CI) formula: $ CI = P \times \left(1 + \frac{R}{100}\right)^n - P $
   - Where $ P = 14,000 $, $ R = 10 $, and $ n = 3 $.

$$
   CI = 14000 \times \left(1 + \frac{10}{100}\right)^3 - 14000
   $$
   $$
   CI = 14000 \times \left(1.1\right)^3 - 14000
   $$
   $$
   CI = 14000 \times 1.331 - 14000
   $$
   $$
   CI = 18634 - 14000
   $$
   $$
   CI = 4634
   $$

3. **Explanation of Options:**
   - **Option 1: Rs. 4634** is correct as calculated above.
   - **Option 2: Rs. 3714** is incorrect because it does not match the calculated compound interest.
   - **Option 3: Rs. 3794** is incorrect because it does not match the calculated compound interest.
   - **Option 4: Rs. 4612** is incorrect because it does not match the calculated compound interest.

Therefore, the correct answer is Option 1: Rs. 4634, as it accurately reflects the compound interest calculated using the given rate and time period.