A debt of Rs. 1,200 is to be paid in one year by making payments of Rs. 100 at the end of each month plus interest at the rate of 1% per month on the outstanding balance. Find the... A debt of Rs. 1,200 is to be paid in one year by making payments of Rs. 100 at the end of each month plus interest at the rate of 1% per month on the outstanding balance. Find the total interest paid.
Understand the Problem
The question is asking to calculate the total interest paid on a debt of Rs. 1,200 over one year, given that payments of Rs. 100 are made at the end of each month, along with interest at the rate of 1% per month on the outstanding balance. This requires understanding the principle of amortization and calculating the interest on a reducing balance.
Answer
The total interest paid is Rs. 66.
Answer for screen readers
The total interest paid over one year is Rs. 66.
Steps to Solve
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Identify the monthly interest and payment plan The principal amount is Rs. 1,200. The monthly payment is Rs. 100, and the interest rate is 1% per month on the outstanding balance.
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Calculate the outstanding balance and interest each month For each month, calculate the interest on the outstanding balance and then deduct the monthly payment. The interest for any month can be calculated as: $$ \text{Interest} = \text{Outstanding Balance} \times 0.01 $$
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Track the payments over the year For each month:
- Calculate the interest
- Subtract the payment
- Update the outstanding balance
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Repeat for 12 months Continue the process for each of the 12 months to determine the total interest paid throughout the year.
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Sum up the total interest Add up the interest calculated for each month to find the total interest paid over the year.
The total interest paid over one year is Rs. 66.
More Information
In an amortization structure, the way the payments are made affects the total interest. Since the payments reduce the outstanding balance, the interest paid decreases over time.
Tips
- Failing to account for the decline in the outstanding balance after each payment.
- Calculating interest on the initial balance instead of the reduced balance after payments.
- Not tracking the interest accrued for each month separately.
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