Problem 4-21 (algorithmic) A good stock-based mutual fund should earn at least 6

Question

Problem 4-21 (algorithmic) 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 200 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 1-6% per year. a. The interest rate Barney and Lynn really earn on their investment is l %. (Round to the one decimal place.)

Explanation / Answer

The rate of interest formula (compound interest, compounded once per year) is given by:

R = (A/P)1/T - 1 ( This will give us the rate of interest in decimals)

Here: R is rate of interest

A is final amount

P is principal amount

T is time in year

Therfore, R = (162,500/32,500)1/25 - 1

= (5)1/25 - 1

= 1.0665 - 1

R = 0.0665

In percentage the rate can be calculated by multiplying it with 100. Therfore rate in percentage is:

0.0665 x 100 = 6.65% per year

Therefore the interest Barney and Lynn rally earn on their investment is 6.6%.

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