Question

Roselin borrowed a sum of 6,000 at the annual interest rate of 15% compounded annually. At the end of each year, she pays back 1,200. What is the total amount she has to pay at the end of the third year in order to clear all her dues?

• A. 6,158.25
• B. 6,000
• C. 5,132.25
• D. 5,950

Answer 1

The Correct Option is A

Finding the Total Amount Roselin Has to Pay at the End of the Third Year

Step 1: Define the Compound Interest Formula 

The formula for compound interest is:

\[ A = P \left(1 + \frac{r}{100} \right)^t \]

Step 2: Given Values

• Principal Amount (\( P \)) = Rs. 6,000
• Annual Interest Rate (\( r \)) = 15%
• Roselin makes an annual payment of Rs. 1,200
• Time Period = 3 years

Step 3: Compute the Amount at the End of Each Year

Year 1:

\[ A_1 = 6000 \times 1.15 = 6900 \]

After paying Rs. 1,200, the remaining balance is:

\[ 6900 - 1200 = 5700 \]

Year 2:

\[ A_2 = 5700 \times 1.15 = 6555 \]

After paying Rs. 1,200, the remaining balance is:

\[ 6555 - 1200 = 5355 \]

Year 3:

\[ A_3 = 5355 \times 1.15 = 6158.25 \]

Final Answer:

Thus, the total amount Roselin has to pay at the end of the third year is Rs. 6,158.25. The correct answer is (A) 6,158.25.