An investor purchases $1000$ worth of units in a mutual fund whose units are valued at $4.00$. The investment dealer takes 9 % front-end-load (deduction) from the gross payment.
One year later the units have a value of $5.00$ and the fund managers claim that the fund"s unit have a value has experienced a 25 % growth in the past year. When units of the fund are sold are sold by an investor, there is a redemption fee of 1.5 % of the value of the units redeemed.
(a) If the investor sells all his units after one year, what is the effective annual rate of interest of his investment?
(b)Suppose instead that after one year the units are valued at $3.75$. What is the return in this case?
I have tried the following,(assuming compound interst)
$A(0)=(1000 * 4)=4000$
New $A(0)=4000-(0.09*4000)=3640$
$A(1)=1000*5=5000$
Since growth factor is $25%$
$\frac{a(1)}{a(0)}=0.25$
$a(0)=1$, so, we have $a(1)=0.25$
$i=\frac{a(1)}{a(0)}-1=0.25-1=-0.75$
My answer is wrong, so I presume the workings are wrong, same logic for (b) should follow. Answer for (a)12.04% (b)-15.97%
Due to the upfront fee your investment is smaller than what you've effectively paid thus lowering your participation from the 25 % raise. Furthermore the redemption fee also lowers your profit.
Taking both into account you paid \$4.000 for 910 shares of the fund (due to the 9 % fee). At the end these are worth \$ 4.550 before fees. Subtracting 1.5 % leaves you with \$4.482. Your return is calculated as $ 4.482/4.000=1.1204 $, i.e. 12.04 %.
Lessons learned: The fees left you with only half of the profit in terms of the fund price!
Same calculation for b) where the fees completely eat up the gains.