Question

Find the amount of an annuity due of Rs $500$ per quarter for $8$ years and $9$ months at $6\%$ compounded quarterly.

• A. Rs $27452.30$
• B. Rs $23137.98$
• C. Rs $13740.86$
• D. Rs $24671.30$

Answer 1

Answer: (B)

Rs $23137.98$

Number of interest periods, $n=4\times 8+3=35$
Each installment, A=Rs $500$
Present value of annuity due,
$v=\frac{A}{r}\times (1+r)\times [1-(1+r{)}^{-n}]$
= $\frac{500}{0.015}\times 1.015\times [1-(1.015{)}^{-35}]$
= $13740.86$
$v=\frac{A}{r}\times (1+r)\times [1-(1+r{)}^{-n}-1]$
= $\frac{500}{0.015}\times 1.015\times [1-(1.015{)}^{-35}-1]$
= $23137.98$