Bunuel wrote:

Bob invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest (compounded annually) for the same 2 years at the same rate of interest and received $605 as interest. What was the annual rate of interest?

(A) 5%

(B) 10%

(C) 12%

(D) 15%

(E) 20%

Although we are not given the amount invested in either of the two bonds,, we know that the two amounts are equal. So we can let P = the amount invested in each bond. We can let r = the interest rate for each bond investment. We can create an equation for the amount of interest earned for the first bond, using the simple interest formula P x r x t = I. :

P x r x 2 = 550

We can also create an equation for the amount of interest earned for the second bond, using the compound interest formula: P(1 + r)^t - P = I:

P(1 + r)^2 - P = 605

Simplifying the first equation, we have P(2r) = 550 and simplifying the second equation, we have P[(1 + r)^2 - 1] = 605.

Dividing the first equation by the second, we see that the P cancels out, and we have:

(2r)/[(1 + r)^2 - 1] = 550/605

605(2r) = 550[(1 + r)^2 - 1]

1210r = 550[1 + 2r + r^2 - 1]

1210r = 1100r + 550r^2

110r = 550r^2

Dividing both sides by 110r, (we can do that since r is nonzero), we have:

1 = 5r

r = 1/5 = 20%

Answer: E