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17 Jun 2017, 10:03
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Kevin invested $8,000 for one year at a simple annual interest rate of 6 percent and invested$10,000 for one year at an annual interest rate of 8 percent compounded semiannually. What is the total amount of interest that Kevin earned on the two investments?

A. $880 B.$1,088
C. $1,253 D.$1,280
E. $1,296 [Reveal] Spoiler: OA _________________ Md. Abdur Rakib Please Press +1 Kudos,If it helps Sentence Correction-Collection of Ron Purewal's "elliptical construction/analogies" for SC Challenges Director Joined: 04 Dec 2015 Posts: 696 Location: India Concentration: Technology, Strategy Schools: ISB '19, IIMA , IIMB, XLRI WE: Information Technology (Consulting) Kevin invested$8,000 for one year at a simple annual interest rate of [#permalink]

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17 Jun 2017, 10:10
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AbdurRakib wrote:
Kevin invested $8,000 for one year at a simple annual interest rate of 6 percent and invested$10,000 for one year at an annual interest rate of 8 percent compounded semiannually. What is the total amount of interest that Kevin earned on the two investments?

A. $880 B.$1,088
C. $1,253 D.$1,280
E. $1,296 Simple interest earned on$8000 with rate of interest 6% for 1 year.

$$SI = \frac{8000 * 6 * 1}{100} = 480$$

Amount earned on $10,000 with rate of interest 8% for 1 year compounded semi annually. Amount $$= \frac{104}{100} * \frac{104}{100} * 10,000 = 10816$$ CI = Amount - Principal CI $$= 10,816 - 10,000 = 816$$ Total amount of interest earned $$=480 + 816 = 1296$$. Answer E... _________________ Please Press "+1 Kudos" to appreciate. BSchool Forum Moderator Joined: 26 Feb 2016 Posts: 2436 Location: India GPA: 3.12 Kevin invested$8,000 for one year at a simple annual interest rate of [#permalink]

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17 Jun 2017, 10:22
1
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From the first investment, she would have earned 480$at 6% interest on a total amount of 8000$

From the second investment, the interest is calculated at half yearly basis
The annual interest is 8%, so half-yearly interest is 4%

For the investment of 10000$, the interest for the first half of the year is 400$.

Since this interest is compounded, the interest of the
second half of the year is calculated for the principal of 10400$Again the interest percentage is 4%, hence the interest for this half year is 4% of 10400 = 104*4 = 416$

Therefore, total interest from both investments is 480 + 400 + 416 = 1296(Option E)

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Re: Kevin invested $8,000 for one year at a simple annual interest rate of [#permalink] ### Show Tags 17 Jun 2017, 13:02 5 This post received KUDOS Expert's post 2 This post was BOOKMARKED AbdurRakib wrote: Kevin invested$8,000 for one year at a simple annual interest rate of 6 percent and invested $10,000 for one year at an annual interest rate of 8 percent compounded semiannually. What is the total amount of interest that Kevin earned on the two investments? A.$880
B. $1,088 C.$1,253
D. $1,280 E.$1,296

You can avoid calculation of compounded interest here.

$8,000 for one year at a simple annual interest rate of 6 percent = 6/100*8,000 =$480.

IF $10,000 were invested for one year at a simple annual interest rate of 8 percent, then it would earn 8/100*10,000 =$800. Since the interest is compounded semiannually, then it would earn interest on interest and actual interest would be higher.

So, the answer should be slightly more than $480 +$800 = $1,280. Only E fits. Answer: E. _________________ Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 2447 Location: United States (CA) Re: Kevin invested$8,000 for one year at a simple annual interest rate of [#permalink]

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15 Nov 2017, 16:57
2
KUDOS
Expert's post
AbdurRakib wrote:
Kevin invested $8,000 for one year at a simple annual interest rate of 6 percent and invested$10,000 for one year at an annual interest rate of 8 percent compounded semiannually. What is the total amount of interest that Kevin earned on the two investments?

A. $880 B.$1,088
C. $1,253 D.$1,280
E. $1,296 We’ll use the simple interest formula for both parts of this question: I = P x r x t , where I = interest, P = principal, r = the annual interest rate, and t = the number of years (or part of a year) for which interest is earned. Let’s first determine what Kevin earned from the$8,000 at 6 percent simple interest for 1 year:

8000 x 0.06 x 1 = $480 Next let’s determine what Kevin earned from the$10,000 for one year at an annual interest rate of 8 percent compounded semiannually. Note that semiannual compounding means that interest is computed twice a year, so for the first half of the year, we use t = 1/2:

10,000 x 0.08 x 1/2 = 10,000 x 0.08 x 1/2 = $400 = interest for the first half of the year. Thus, the new principal is 10,000 + 400 =$10,400. This new principal earns interest for the second half of the year:

10,400 x 0.08 x 1/2 = $416 So, the total interest earned on the$10,000 was 400 + 416 = 816.

From the two investments, therefore, Kevin earned 480 + 816 = $1,296 in interest. Answer: E _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 11496 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: Kevin invested$8,000 for one year at a simple annual interest rate of [#permalink]

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20 Nov 2017, 17:58
1
KUDOS
Expert's post
Hi All,

We're told that Kevin made two investments:
1) $8,000 for one year at a simple annual interest rate of 6 percent 2)$10,000 for one year at an annual interest rate of 8 percent compounded semiannually.

We're asked for the total amount of interest that Kevin earned on the two investments. This question requires that we use the two interest formulas:
Simple Interest = Principal x (1+rt)
Compound Interest = Principal x (1+r)^t
Where r and t are the interest rate/year and the amount of time (in years).

The first investment = $8,000(1.06) =$8,480 --> $480 in interest The second investment calculates the interest SEMI-ANNUALLY, so we have to double the value of t, but halve the value of r.... The second investment =$10,000(1.04)^2

While that calculation might look a bit 'complex', we don't actually have to complete it. The first interest payment would equal $400 (since that is 4% of$10,000), but the second payment would be slightly HIGHER (since we'd be taking 4% of $10,400). Thus, the TOTAL interest would equal$480 + $400 + (a little more than$400) = More than $1280. There's only one answer that matches... Final Answer: [Reveal] Spoiler: E GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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