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

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Bob invested one half of his savings in a bond that paid simple intere [#permalink]

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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%

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Re: Bob invested one half of his savings in a bond that paid simple intere [#permalink]

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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%

Kudos for a correct solution.


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.
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Re: Bob invested one half of his savings in a bond that paid simple intere [#permalink]

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New post 21 Apr 2015, 09:37
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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%

Kudos for a correct solution.


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.
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Re: Bob invested one half of his savings in a bond that paid simple intere [#permalink]

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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%

Kudos for a correct solution.


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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Bob invested one half of his savings in a bond that paid simple intere [#permalink]

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New post 06 Dec 2017, 14:14
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
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Bob invested one half of his savings in a bond that paid simple intere [#permalink]

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New post 28 Mar 2018, 08:38
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
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Re: Bob invested one half of his savings in a bond that paid simple intere [#permalink]

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New post 09 Apr 2018, 16:30
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
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Re: Bob invested one half of his savings in a bond that paid simple intere   [#permalink] 09 Apr 2018, 16:30
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