Q.If the payment of $\text{\text{₹}}\,2{,}000$ is made at the end of every quarter for 10 years at the rate of 8% per year, then find the amount of annuity. $[(1.02)^{40}=2.2080]$

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:

$A=\frac{a}{i}\big[(1+i)^n-1\big].$

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