Calculating the Annual Instalment for Simple Interest Debt

This problem asks us to find the amount of the equal annual instalment required to pay off a debt of ₹8,432 within 4 years, given that the interest rate is 16% simple interest per annum. We need to calculate the 'annual instalment' that covers both the principal amount and the simple interest accrued over the period.

Understanding Simple Interest Instalment Calculation

When dealing with loans or debts repaid through equal instalments under simple interest, the total amount to be repaid is the original debt plus the total simple interest calculated on it. The formula helps determine the equal periodic payment (in this case, annual) needed.

Formula for Equal Annual Instalment (Simple Interest)

The formula to calculate the equal annual instalment (let's denote it as E) to discharge a debt (D) in n years at a simple interest rate (r) per annum is:

$$ E = \frac{D}{n + \frac{n \times (n-1) \times r}{2}} $$

Where:

• D = Total Debt = ₹8,432
• n = Number of years = 4
• r = Rate of simple interest per annum = 16% = 0.16

Step-by-Step Calculation

Let's plug the given values into the formula:

1. Calculate the term $\frac{n\times (n-1)}{2}$:
   $$ \frac{4 \times (4-1)}{2} = \frac{4 \times 3}{2} = \frac{12}{2} = 6 $$
2. Calculate the interest component in the denominator $\frac{n\times (n-1)\times r}{2}$:
   $$ 6 \times r = 6 \times 0.16 = 0.96 $$
3. Calculate the denominator $n+\frac{n\times (n-1)\times r}{2}$:
   $$ 4 + 0.96 = 4.96 $$
4. Calculate the annual instalment $E$:
   $$ E = \frac{8432}{4.96} $$
   $$ E = 1700 $$

Conclusion

Therefore, the annual instalment required to discharge the debt is ₹1,700.