What annual payment will discharge a debt of Rs. 7620 due in 3 years at 16+2/3% per annum compound interest?

To calculate the annual payment required to discharge a debt of Rs. 7620 due in 3 years at 16 ⅔% per annum compound interest, we can follow these steps:

### Step 1: Convert the interest rate
The interest rate is given as 16 ⅔%, which can be written as:

\[
16 \frac{2}{3} \% = \frac{50}{3} \% = \frac{50}{300} = 0.1667
\]

### Step 2: Apply the formula for compound interest
The formula for compound interest is:

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

Where:
- \( A \) is the amount (Rs. 7620),
- \( P \) is the principal (the unknown here),
- \( r \) is the rate of interest (16 ⅔% or 0.1667),
- \( n \) is the number of years (3).

### Step 3: Substitute the known values and solve for \( P \)

\[
7620 = P \left(1 + \frac{50}{300}\right)^3
\]

\[
7620 = P \left(1 + 0.1667\right)^3 = P \times 1.1667^3
\]

Now we calculate \( 1.1667^3 \):

\[
1.1667^3 = 1.5934
\]

Thus, the equation becomes:

\[
7620 = P \times 1.5934
\]

Solve for \( P \):

\[
P = \frac{7620}{1.5934} = 4783.13
\]

So, the principal \( P \) is approximately Rs. 4783.13.

### Step 4: Calculate the annual payment

Since the debt is repaid in equal annual payments, we now use the formula for annual payments of a compound interest loan:

\[
A = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1}
\]

Where:
- \( P = 4783.13 \),
- \( r = 0.1667 \),
- \( n = 3 \).

Substituting the values:

\[
A = \frac{4783.13 \times 0.1667 \times (1 + 0.1667)^3}{(1 + 0.1667)^3 - 1}
\]

Now I will calculate this step.

Let me do that for you.The annual payment required to discharge the debt is approximately Rs. 2153.15.

Would you like more details or have any questions?

Here are 5 related questions you might find useful:
1. How does compound interest differ from simple interest in loan repayments?
2. How would the annual payment change if the interest rate increased to 20%?
3. What is the formula for calculating the future value of an investment under compound interest?
4. How would the annual payment change if the loan term was extended to 5 years?
5. What is the significance of compound frequency in calculating interest?

**Tip:** When dealing with compound interest, always make sure the interest rate and the compounding period are consistent (e.g., annual interest with annual compounding).

Discover how to calculate the annual payment required to discharge a debt of Rs. 7620 due in 3 years at 16 ⅔% per annum compound interest. This step-by-step guide covers key concepts such as compound interest and loan repayments, ideal for students in Grades 10-12.

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