The Periodic payment of Rs. R, in a sinking fund required to accumulate a sum of Rs. \( A \) over \( n \) periods with interest charged at a rate \( i \) per period per rupee is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \displaystyle\frac{\mathrm{A}i}{(1+i)^n-1} \)
A sinking fund is built by equal payments R at the end of each period, so it is an ordinary annuity. Its future value after n periods must equal A:
\( \displaystyle A=R\left[\frac{(1+i)^n-1}{i}\right] \)
Solving for R:
\( \displaystyle R=\frac{Ai}{(1+i)^n-1} \)
Tip: A sinking fund (saving towards a future amount) uses the future value factor \( (1+i)^n-1 \); a loan EMI (repaying a present amount) uses the present value factor \( 1-(1+i)^{-n} \).