Roger's edge fund is taking x dollars and investing in bonds

AAPL wrote:Roger's hedge fund is taking x dollars and investing in bonds that yield r percent in simple interest. The amount of interest earned over 2 years is $1000. In terms of x, what dollar amount invested will yield $4000 over 5 years, assuming the bond's yield remains the same?

A. x
B. 2x/3
C. 2x
D. 4x/3
E. 8x/5

We use the simple interest formula: interest = principal x rate x time. Letting x = the principal and expressing the interest rate as a decimal, we can create the equation:

(x)(r/100)(2) = 1000

xr = 50,000

r = 50,000/x

For a 5-year period,, letting p = the new principal, the amount of interest earned will be:

(p)[(50,000/x)/100](5) = 4000

(p)(500/x) = 800

p = 800/(500/x)

p = 800x/500 = 8x/5

Alternate Solution:

Let’s first find the interest paid to x dollars over a period of 5 years. Since 5 is 2.5 times 2, the interest paid to x dollars in 5 years should also be 2.5 times the interest paid to x dollars in 2 years; i.e. 2500 dollars.

Now, let’s denote the amount required to earn 4000 dollars in 5 years by y and set up a simple proportion:

x/2500 = y/4000

y = 4000x/2500 = 8x/5

Answer: E