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

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

CHECK VERITAS PREP OFFICIAL SOLUTION HERE:

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

QUESTION:

Why did you divide the first equation by the second?

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

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

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

Does that help?

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

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.

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.

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!

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

thanks

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

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.

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

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