Quote:
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%
Let the amount invested in each bond = $100
We can PLUG IN THE ANSWERS, which represent the simple interest.
When the correct answer is plugged in:
\(\frac{simple-interest}{compound-interest }= \frac{550}{605} = \frac{110}{121} = \frac{10}{11}\)
The numerator of the fully reduced fraction suggests that the correct answer is probably a multiple of 10.
B: 10%
Simple interest:
First-year interest = 10% of 100 = 10
Second-year interest = 10% of 100 = 10
Total interest = 10+10 = 20
Compound interest:
First-year interest = 10% of 100 = 10
Amount at the end of the first year = 100+10 = 110
Second-year interest = 10% of 110 = 11
Total interest = 10+11 = 21
Resulting ratio:
\(\frac{simple}{compound} = \frac{20}{21}\)
The required ratio is not yielded.
Eliminate B.
E: 20%
Simple interest:
First-year interest = 20% of 100 = 20
Second-year interest = 20% of 100 = 20
Total interest = 20+20 = 40
Compound interest:
First-year interest = 20% of 100 = 20
Amount at the end of the first year = 100+20 = 120
Second-year interest = 20% of 120 = 24
Total interest = 20+24 = 44
Resulting ratio:
\(\frac{simple}{compound }= \frac{40}{44} = \frac{10}{11}\)
Success!