Investment problem?

Question

Suppose that you invested $16,000 in a high-risk growth fund that after 2 years was worth $25,000. Your broker used the following equation to find the average annual rate of return, r

16,000(1 + r)^2 = 25,000

What is the annual rate of return?

Hint: Rewrite the equation in standard form, then solve by factoring.
Write your final answer as a %. (there is no negative rate of return so the answer will be positive).

Answer 1

25%. You take 25000/16000 = (1+r)^2...then take the square root on both sides and subtract 1. This yields 25%. Not too shabby.

Answer 2

The easy way it to get (1+r)^2 by itself and take the square root of both sides:

16000 * (1+r)^2 = 25000
(1+r)^2 = 25/16
1+r = +/- 5/4

Discarding the negative answer,

1+r = 5/4
r = 1/4

Expressed as a percentage:

r = 25%

Checking the result:

Start with $16,000.
At the end of one year you'd have $16,000 * (1.25), which is $20,000.
At the end of two years you'd have $20,000 * 1.25, which is $25,000.

If you had to use standard form and factoring, it would be:

(1+r)^2 = 25/16
r^2 + 2r + 1 = 25/16
r^2 + 2r - 9/16 = 0
(r - 1/4)(r + 9/4) = 0
r = 1/4 or r = -9/4

Answer 3

16,000(1 + r)^2 = 25,000 divide both sides by 16,000
(1+r)^2=1.5625 take square root of both sides
1+r=1.25 subtract 1 from each side
r=0.25 or 25%

The method you suggest will also work, but in this particular case, the square was already completed making this method easier as I'm sure you will agree. Think outside the box!

Answer 4

(1+r)^2 =25000/16000 =1.5625
1+2r +r^2 =1.5625
r^2 +2r -.5625 = 0

16000 +32000r +16000r^2 = 25000
16r^2 +32r +16 -25 = 0
16r^2 +32r -9 =0
(4r -1)(4r +9) = 0
4r = -9 (not applicable)
4r =1
r=1/4 = .25 the interest rate is 25%

Answer 5

25%
...I did this on my calculator. Graph y=16000(1+x)^2 and y=25000
Find where the intersect on the positive side. multiply your answer by 100 (for the %)