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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

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17 Jun 2017, 13:02
17
8
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.

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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, 10:10 13 4 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 $$=480 + 816 = 1296$$.

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Re: Kevin invested $8,000 for one year at a simple annual interest rate of [#permalink] Show Tags 17 Jun 2017, 10:22 5 1 4 From the first investment, she would have earned 480$ 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) _________________ You've got what it takes, but it will take everything you've got Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 7393 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
5
2
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 Scott@TargetTestPrep.com 122 Reviews 5-star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 14812 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 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
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: 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 *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: Kevin invested $8,000 for one year at a simple annual interest rate of [#permalink] Show Tags 04 Jul 2018, 22:10 ($$\frac{6}{100}$$)(8,000) = (6)(80) =$480

($$\frac{4}{100}$$)(10,000) = (4)(400) = $400 (In the second half of the year the principal will be$10,000 + $400 =$10,400)

($$\frac{4}{100}$$)(10,400) = (4)(104) = $416 480 + 400 + 416 = 480 + 816 =$1,296

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Re: Kevin invested $8,000 for one year at a simple annual interest rate of [#permalink] Show Tags 19 Jan 2019, 02:37 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

PS02209

SI = p*r*t/100
= 8000*.06*1 = 480
CI= P ( 1+r/100) ^t
semiannually = 10000(1+.04)^2 = 10816; interest 816
total interest earned = 480+816 = 1296
IMO E
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Re: Kevin invested $8,000 for one year at a simple annual interest rate of [#permalink] Show Tags 15 May 2019, 10:36 8000 x 0.06 x 1 =$480
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.
Now principal is 10,000 + 400 = 10,400.
10,400 x 0.08 x 1/2 = $416 = interest for the second half of the year. Total interest for one year = 400 + 416 = 816. Total interest from both investment = 480 + 816 = 1,296 Ans E Re: Kevin invested$8,000 for one year at a simple annual interest rate of   [#permalink] 15 May 2019, 10:36
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