Problem Solving

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%

Answer: E

Source: Veritas Prep

Simple interest for 2 years = $550
Simple interest for 1 year = 550/2 = $275


Investing in another bond in which the interest is compounded annually and received $605
Therefore, interest gotten from 1st year = 605 - 550 = $55

Let the rate of interest = R
R% of 1 year simple interest = $55
R% of 275 = 55
R/100 * 275 = 55
275R/275 = 5500/275
R = 20%

Answer = E

Rate of interest = r
r% of 275 = 55
r/100 * 275 = 55
275r/275 = 5500/275
r= 20%

E

M7MBA wrote: ↑

Thu Aug 20, 2020 9:00 am

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:
(simple interest)/(compound interest) = 550/605 = 110/121 = 10/11
The numerator of the blue fraction suggests that the correct answer is likely to be 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:
simple/compound = 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:
simple/compound = 40/44 = 10/11
Success!

The correct answer is E.