Bob invested one half of his savings in a bond that paid simple intere

Question

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%

Kudos for a correct solution.

(A) 5%
(B) 10%
(C) 12%
(D) 15%
(E) 20%

Lucky2783 · Accepted Answer

For the first year SimpleInterest and Compound interest will always be same if compounding is done annually. 
So, the difference  605 - 550 = 55  is attributed to 275$ which accumulated at the end of 1st year in the CompoundInterest account.

275 * \frac{R}{100} = 55

R=20% 
Answer E.

JeffTargetTestPrep · Answer

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  = 605. Dividing the first equation by the second, we see that the P cancels out, and we have:
(2r)/  = 550/605

605(2r) = 550

1210r = 550

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

funkyleaf · Answer

First divide $550/2years to get 275$/yr non-compounding interest.

Next, subtract from the total compound after 2 years to see the interest gained in the second year. This can be done because the same amount has been invested in both accounts and the interest gained for the first year will be the same. So, $605-$275= $330.

To find the difference in interest gained, $330-$275= $55 increase in interest after the first year through compounding.

From this information we can set up the equation $275 * X% = $55... 55/275=1/5=20% giving us answer choice E.

Bunuel · Answer

CHECK VERITAS PREP OFFICIAL SOLUTION  HERE :

Madhavi1990 · Answer

Used hit and trial. 
605 - 550 = 55 dollars

a) 5% of x is 25. So tried 10% (option B) --> it is $550

10% *550+500 = 605

Total interest = 10%+ 10%= 20 % interest

testcracker · Answer

in the first year interest earned from both bonds will remain the same, thus
interest earned from both bonds in the first year is

550 / 2 = 275

so, in the second year, interest earned from the bond that pays compounded interest will be (605 - 275) = 330

now, the extra amount (330 - 275) = 55 is the interest earned on the interest of previous year's interest

so, 55 = i * 275

=) i = 55 / 275

thus interest rate is 1/5 = 20 % = E the answer

thanks

GMAT2645 · Answer

QUESTION:

Why did you divide the first equation by the second?

GMAT2645 · Answer

When it asks for the "annual rate of interest" I am under the assumption that there are two different bonds--(1) one that pays simple interest and (2) one that pays compound interest. How can there only be one annual rate of interest? Thank you.

GMAT2645 · Answer

Believe I may have answered my own question. One of the insights is to realize that though given two equations and two unknowns (P and r), the Ps cancel out leaving two equations and one unknown, therefore, one can solve for r, that annual rate of interest? Thanks.

Lampard42 · Answer

The difference between the interests under Compounding and Simple interest is just interest on interest for the second year as Interest under both methods is same for 1st period under compounding.

from Simple interest 2PR/100 = 550 ; PR = 50*550
Interest on interest = PR*R = 605-550 ; 550*50R = 55 ; R= 1/5 = 0.20 IMO Option E

GMATGuruNY · Answer

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!

E

dave13 · Answer

HI BrentGMATPrepNow can you please say what is the logic behind division of simple interest by compound one. pls see highlighted part thanks

BrentGMATPrepNow · Answer

Here's what we know: 
2Pr = 550
P(1 + r)^2 - P = 605

Notice that we can factor P out of the second equation to get
2Pr = 550
P  = 605

At this point we can see that, if we divide the bottom equation into the top equation, the variable P cancels out leaving us with: (2r)/  = 550/605

This technique is useful, since we now have an equation with just one variable, r.

Does that help?

frp · Answer

Hey  Bunuel , are there any similar questions? If so, can you please share them? Thanks!

Bunuel · Answer

4. Percents and Iterest 
     Theory   
 Math: Number Theory - Percents 
 Percentages, Interest and More 
     Questions   
 Compound Interest Problems 
 DS Questions 
 PS Questions

For more check:
 ALL YOU NEED FOR QUANT ! ! ! 
 Ultimate GMAT Quantitative Megathread

Hope it helps.

Kinshook · Answer

Given: 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.

Asked: What was the annual rate of interest?

Simple interest for one year = $550/2 = $275
Compound interest on $275 = (605-550) = $55
$275*R = $55
R = 55/275 = 20%

IMO E

Asked: What was the annual rate of interest?

Simple interest for one year = $550/2 = $275
Compound interest on $275 = (605-550) = $55
$275*R = $55
R = 55/275 = 20%

IMO E

blonpina · Answer

The solution is brilliant! It reminds how important is to approach smart to the problems. I solved it in a much more ugly and time consuming way using system of equations:

x - nominal
y - percent/100

(1) x * (1+2y) - x = 550
(2) x * (1+y)^2 - x = 605

taking x from the brackets:

(1) x(1+2y-1) = 550
(2) x((1+y)^2-1) = 605

divide (1) by (2), cancel x and get the result y=0.2 which is 20%

mini97 · Answer

what is hit and trial?

Goldenfuture · Answer

2 min thing only difference is extra interest on 1st year interest which will be 605-550 = 55
& SI for 1st year =550/2 = 275
sp 275(R/100) = 55
r= 100/5=20%

Bob invested one half of his savings in a bond that paid simple intere

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Bob invested one half of his savings in a bond that paid simple intere

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards