Question

An 8-year annuity due has a present value of 1,000$.Iftheinterestrateis$5$ percent, the amount of each annuity payment is closest to which of the following?

• A. 154.73$
• B. 147.36$
• C. 109.39$
• D. 104.72$
• E. 99.74$

Answer 1

Answer: (A)

154.73\Rightarrow$Wehave,$V=\$1000,n=8$ and $r=5\%=0.05$.

$\Rightarrow$ We know, $V=\frac{A}{r}\times [1-(1+r{)}^{-n}]$

$\Rightarrow$ $A=\frac{V\times r}{[1-(1+r{)}^{-n}]}$

$\Rightarrow$ $A=\frac{1000\times 0.05}{[1-(1.05{)}^{-8}]}$

$\Rightarrow$ $A=\$154.73$