Answer to Question #181973 in Financial Math for Anamika

Question

9.X is entitled to the following benefits :

Five annual payments at the rate of Rs. 200 p.a., the first being due at the beginning of second year from now.

Thereafter 6 annual payments at the rate of Rs. 300 p.a., the first of these being due at the beginning of 11 years from now.

An additional lump sum of Rs. 2,000 at the end of 9 years.

10. Find the PV of his benefits at the rate of interest of 3.03% p.a. compounded monthly.

A sum of Rs. 45,000 invested will provide payments of Rs. 600 each at the end of every 4 months. Find the underlying rate of interest compounded semi annually.

Answer 1

(9)

Present Value of annuity = Annuity * PVAF ( Periodic rate, Number of periods )

Present value of cash flow = Cash flow * PVIF ( Periodic rate, Number of periods )

Effective Annual rate = [ 1 + Monthly rate ]^{Number of months} - 1

$= [ 1 + [\frac{ 0.0303}{12}]^ { 12 } -1$

$= [ 1.002525 ]^{12} - 1$

$= 1.03072 - 1$

$= 0.03072$ $or 3.072\%$

Five annual payments

$=200 * PVAF [ 3.072\%, 5 ]$

$PVAF [ 3.072\%, 5 ]= [\frac{ 1}{1.03072} + \frac{1}{1.03072^2}+ \frac{1}{1.03072^3}+\frac{1}{1.03072^4}+ \frac{1}{1.03072^5}]= 4.5703$

Therefore, five annual payments will be

$= 200 *\times 4.5703$

=914.06

Six annual payments

$300 \times PVAF [ 3.072\%, 6 ] \times PVIF ( 3.072\%, 9 )$

$PVAF [ 3.072\%, 6 ] =[ \frac{1}{1.03072}+\frac{1}{1.03072} + \frac{1}{1.03072^2}+ \frac{1}{1.03072^3}+\frac{1}{1.03072^4}+\frac{1}{1.03072^5}+$

$\frac{1}{1.03072^6} ]=$ 5.4043

$PVIF ( 3.072\%, 9 )= [ \frac{1}{1.03072^9} ]=0.76161$

Therefore six annual payments will be

$300\times 5.4043\times 0.761611==1,234.79$

Lumpsum

$=2000 \times PVIF ( 3.072\%, 9 )$

$= 2000 * 0.76161$

$=1,523.22$

Total present value

$=914.06+1234.79+1523.22= 3,672.07$

(10)

Assume t=1 so,

A year 600*3=1800

$A=P(1+ \frac{r}{n})^{nt}$

$46800=45000(1+\frac{r}{3})^3$

$1.04=(1+\frac{r}{3})^3$

$3√1.04 =1+\frac{r}{3}$

$1.013159404=1+\frac{r}{3}$

$r=0.039478211$

semi annually interest.

$r=3.9478211\times1.5=5.9217317$