Q.If '$a$' is the annual payment '$n$' is the number of periods and '$i$' is compound interest for $\text{\text{₹}}\,1$ then future amount of the ordinary annuity is :

The future amount of an ordinary annuity is $A=\dfrac{a}{i}\big[(1+i)^n-1\big]$. In an ordinary annuity an equal payment $a$ is made at the end of each period, for $n$ periods, and each payment earns compound interest at rate $i$ per period. The accumulated value (future amount) is the sum of a geometric series of these compounded payments, which gives: $A=\frac{a}{i}\big[(1+i)^n-1\big].$ Option (c), $P=\dfrac{a}{i}(1+i)\big[1-(1+i)^{-n}\big]$, is a present-value form, and option (a) is unrelated — so the c …