What annual instalment will discharge a debt of Rs. 2,106 due in 3 years at 8% simple interest per annum? (Note: instalments will be paid at the end of year 1, year 2 and year 3.)

Given:

Principal = Rs. 2106

Time = 3 years

Rate = 8%

Formula used:

Annual instalment = \(\frac{Principal \times 100}{100 \times Time + \frac{Rate \times Time (Time-1)}{2}}\)

Calculation:

Annual instalment = \(\frac{2106 \times 100}{100 \times 3 + \frac{8 \times 3 (3-1)}{2}}\)

= \(\frac{2106 \times 100}{300 + {4 \times 3 (2)}}\)

= \(\frac{2106 \times 100}{300 + 24}\)

= \(\frac{2106 \times 100}{324}\)

= 650

Answer is 650.

Explanation:

Annual Instalment Calculation:

• To calculate the annual instalment required to discharge a debt of ₹2,106 over 3 years at 8% simple interest per annum, we divide the repayment into three equal instalments, including interest accrued on the remaining principal.

Equation for Total Instalments:

\(\left(x + \frac{16x}{100}\right) + \left(x + \frac{8x}{100}\right) + x = 2106\)

Combine terms:

\(3x + \frac{24x}{100} = 2106\)

Simplify further:

\(3.24x = 2106\)

Solve for (x):

\(x = \frac{2106}{3.24}\)

\(x = 650\)