A good stock-based mutual fund should earn at least 6% per year over a long peri
ID: 1135629 • Letter: A
Question
A good stock-based mutual fund should earn at least 6% per year over a long period of time. Consider the case of Barney and Lynn, who were overheard gloating (for all to hear) about how well they had done with their mutual fund investment." We turned a $32,500 investment of money in 1982 into $162,500 in 2007." a. What return (interest rate) did they really earn on their investment? Should they have been bragging about how investment-savvy they were? b. Instead, if $1,300 had been invested each year for 25 years to accumulate $162,500, what return did Barney and Lynn earn? Click the icon to view the interest and annuity table for discrete compounding when i-6% per year. a. The interest rate Barney and Lynn really earn on their investment is 6.6 %. (Round to the one decimal place.) Barney and Lynne should have been bragging about how investment-savvy they were. b. The interest rate Barney and Lynn earn on their investments is Round to the one decimal place.)Explanation / Answer
Solution:
a) The rate of return can be found using following formula
FV = PV(1+r)^n
162,500 = 32,500(1+r) ^ 25
5 = (1+r) ^ 25
(1+r) = 5 ^ (1/25)
1 + r = 1.0664949
r = 0.0664949
r = 6.64%
The interest rate Barney and Lynn really earn on their investment = 6.64%
So r = 6.6%
Barney and Lynne should have been bragging because they are earning return of 6.64% that is more than 6% standard return.
b)
We can use the Future value of annuity formula to calculate rate of return earned by Barney and Lynn
The formula is as under,
FV = P*{[(1+r)^n - 1] / r}
FV = Future value = $162500
P = Annuity Amount = $1300
n - no.of years = 25 years
r = Interest rate = ?
162500 = 1300*{[(1+r)^25 - 1] / r}
125 = {[(1+r)^25 - 1]/r}
By solving above equation by trial and error method we get
r = 0.1158
Interest rate = 11.58%