Problem Solving

An investment with the Brown company yields 10% compounded annually over 2 years, while an investment with Green Corp. yields 20% annually over the same period. If Fernando invests a given amount in Green Corp, by what percent should Rita's initial investment exceed Fernando's, if she wants to invest in Brown but match the final value of his investment?

17
18
19
20
21

C

Hi,
Assuming that the investment with Green Corp. to be compound interest as well.
Let their investment be x and y.
After 2 years there values will be x(1.1)^2 and y.(1.2)^2. They are equal
So, 1.21x=1.44y => x= 1.19y
So, Rita's initial investment should exceed Fernando's by 19%

Hence, C

I want to point out that the wording of the question isn't very clear. It specifies that the Brown investment compounds annually, but doesn't specify that the Green investment does. I solved it both ways, and the answer I get when I used simple compounding for Green didn't show up as a choice, so they meant annual compounding for both.

Final value of Brown = b*1.1^2, where b is initial investment
Final value of Green = g*1.2^2, where g is initial investment

We want the final investment value to be the same so set the equations equal to each other
b*1.21 = g*1.44
b/g = 1.44/1.21
b/g ~ 1.19 (I say approximate because 1.44/1.21 isn't a terminating decimal)

So b must exceed g by about 19%.

Is there an easy way to do the calculation of 1.44/1.21? I'm not seeing any help by prime factorization.

djiddish98 wrote:Is there an easy way to do the calculation of 1.44/1.21? I'm not seeing any help by prime factorization.

Not that I know of... if anyone has one I'd love to hear it

djiddish98 wrote:Is there an easy way to do the calculation of 1.44/1.21? I'm not seeing any help by prime factorization.

Hi,
You can probably write (1.2)^2-(0.01)^2 = (1.21)(1.19) because the denominator is 1.21
So, (1.44-0.0001)/1.21 = 1.19 as we can neglect 0.0001 compared with 1.44.

frank- how did u interpret the statement "by what percent should Rita's initial investment exceed Fernando's,"?


i got 2 numbers 1.21 and 1.44 but did not know what to do with it.

bblast wrote:An investment with the Brown company yields 10% compounded annually over 2 years, while an investment with Green Corp. yields 20% annually over the same period. If Fernando invests a given amount in Green Corp, by what percent should Rita's initial investment exceed Fernando's, if she wants to invest in Brown but match the final value of his investment?

17
18
19
20
21

C

Assuming that each investment is compounding annually and that the question is asking by approximately what percent R's investment should exceed F's:

Let F = 100.
After 1 year, F = 100 + .2*100 = 100 + 20 = 120.
After 2 years, F = 120 + .2*120 = 120 + 24 = 144.

Now we can plug in the answers, which represent by approximately what percent R's investment should exceed F's:

Answer choice C: 19%
R = 100 + .19*100 = 119.
After 1 year, R = 119 + .1*119 = 119 + 11.9 = 130.09 ≈ 131.
After 2 years, R = 131 + .1*131 = 131 + 13.1 = 144.1 ≈ 144.

The correct answer is C.

bblast wrote:frank- how did u interpret the statement "by what percent should Rita's initial investment exceed Fernando's,"?


i got 2 numbers 1.21 and 1.44 but did not know what to do with it.

Hi,
It is analogous to "by what percent does 150 exceed 100". We simply say 50%. After first reading, you might have been confused. But, try to think again on these lines, you might get the logic.