Question

Appendix B

$Appendix_B.jpg$

Appendix D

$Appendix_D.jpg$

You buy a mutual fund for $1,000. It annually distributes $80 for six years, after which you sell the shares for $925. What is the annualized return on your investment? Use Appendix B and Appendix D to answer the question. Round your answer to the nearest whole number.

Answer 1

Present value of future cash inflows at annualized return of your investment should be equals to the purchase price of investment.

$P = A*PVIAF(r,n)+F*PVIF(r,n)$

where,

P = purchase price

F = sale price

r = rate of return

n = no. of years

Thus,

$1,000 = 80*PVIAF(r,6)+925*PVIF(r,6)$

We can find r with trial and error method:

check at r=6%.

$= 80*PVIAF(0.06,6)+925*PVIF(0.06,6)$

$= 80*4.917+925*0.705$

$= 393.36+925*0.652.125$

$\large = \$1,045.485$

At 6%, present value is greater than $1,000 thus check for higher rate.

Check at r=7%

$= 80*4.766+925*0.666$

$\large = \$997.33$

At 7%, Present value is less than $1,000

Thus, We can say that r lies between 6% to 7%.

Now, we can calculate the r with interpolation method.

$\large r = r_L + \frac{\textup{PV at }r_L - 1,000}{\textup{PV at} r_L - \textup{PV at } r_H}$

$r = 6\% + \frac{1,045.485 - 1,000}{1,045.485 - 997.33}$

$r = 6\% + 0.95\%$

$\bg_green \large r = 6.94\%$

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.