Question

Find the present value (in Rs) of a sequence of annual payments of Rs $10000$ each, the first being made at the end of $5^{th}$ year and the last being made at the end of ${12}^{th}$ year, if money is worth $6\%$.

• A. $40187.38$
• B. $49087.38$
• C. $40107.38$
• D. $49187.38$

Answer 1

Answer: (D)

$49187.38$

Here, we have a deferred annuity of $8$ terms(n), deferred for $4$ terms.Each installment, A=Rs $10000$
Rate of interest, $r=$ $6\%$= $0.06$
m= $4$, $m+n=$ $12$
Using the formula, present value
$V=\frac{A}{r}$ $\times \frac{1}{(1+r{)}^m}$ - $\frac{1}{(1+r{)}^{m+n}}$
$V=\frac{10000}{0.06}\times \left[\right(1.06{)}^{-4}-\left(1.06{)}^{-12}\right]$$=49187.38$