Question

Veena is allotted an LIG flat for which she has to make an immediate payment of 100,000$and$10$semi-annualpaymentsof$ $50,000$ each, the first being made at the end of $3$ years. If money is worth $10\%$ per annum compounded half-yearly, find the cash price (in $) of the flat.

• A. $302,509$
• B. $400,509$
• C. $302,009$
• D. $402,509$

Answer 1

The correct option is D $402,509$

$\Rightarrow$ Cash price = Down payment + Present value of annuity --- ( 1 )

$\Rightarrow$ Here, down payment is $\$100,000$, while we have annuity 10 terms i.e. $n$, deferred for $2\frac{1}{2}$ years i.e. 5 terms.

$\Rightarrow$ Each installment, $A=\$50,000$

$\Rightarrow$ Rate of interest, $r=10\%p.a.$ compounded half-yearly = 0.05

$\Rightarrow$ $m=5$ and $m+n=15$

$\therefore$ Present value of annuity,

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

$\Rightarrow$ $\frac{50,000}{0.05}\times \left[\right(1.05{)}^{-5}-\left(1.05{)}^{-15}\right]$

$\Rightarrow$ $\$302509.07$

Now, from ( 1 )

$\Rightarrow$ Cash price of the flat = $\$100,000+\$302,509=\$402,509$