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Question Stats: 74% (02:00) correct 26% (02:01) wrong based on 1298 sessions

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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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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 14 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 $8,000 for one year at a simple annual interest rate of [#permalink] ### Show Tags 6 1 4 From the first investment, she would have earned 480$ 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 D Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 7717 Location: United States (CA) Re: Kevin invested$8,000 for one year at a simple annual interest rate of  [#permalink]

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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 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 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 V Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 15009 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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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 Follow Special Offer: Save$75 + GMAT Club Tests Free
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www.empowergmat.com/
Intern  B
Joined: 11 Sep 2013
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Schools: CBS '19
Re: Kevin invested $8,000 for one year at a simple annual interest rate of [#permalink] ### Show Tags ($$\frac{6}{100}$$)(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 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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Concentration: General Management, Entrepreneurship
WE: General Management (Energy and Utilities)
Re: Kevin invested $8,000 for one year at a simple annual interest rate of [#permalink] ### Show Tags 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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