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. $[(1.02)^{40}=2.2080]$

With quarterly $i=0.02$, $n=40$, $P=₹2000$, the amount of the annuity is $₹1{,}20{,}800$.

Given. $P=₹2000$ at the end of each quarter, $10$ years, $8\%$ p.a.

Quarterly: $\ i=\dfrac{8\%}{4}=0.02,\ n=10\times4=40.$

Amount of an immediate annuity:

$A=P\left[\frac{(1+i)^{n}-1}{i}\right]=2000\left[\frac{(1.02)^{40}-1}{0.02}\right].$

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