Discussion
How much should be the annual installment to completely pay off a debt of Rs. 1078 in 6 years at 9% per annum rate of interest?
Answer: A
Carry the debt and the installments forward to the end of year 6. The debt accrues 6 years of interest; the installments earn interest for 5, 4, 3, 2, 1 and 0 years.
\[ x\left[6 + \frac{9}{100}(5+4+3+2+1+0)\right] = 1078\left(1 + \frac{9 \times 6}{100}\right) \]
\[ x(6 + 1.35) = 1078 \times 1.54 \]
\[ 7.35\,x = 1660.12 \quad\Longrightarrow\quad x = \text{Rs. } 146.67 \]
The same result comes from the standard formula
\[ x = \frac{100 \times \text{Debt}}{100n + R \cdot \frac{n(n-1)}{2}} = \frac{107800}{600 + 135} = 146.67 \]
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