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Buy "All-In-One Standard ($149)", get free Daily quiz (2 mon). Coupon code : SPECIAL Kevin invested$8,000 for one year at a simple annual interest rate of

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Kevin invested $8,000 for one year at a simple annual interest rate of [#permalink] Show Tags 17 Jun 2017, 09:03 3 1 Top Contributor 28 00:00 Difficulty: 35% (medium) Question Stats: 77% (02:00) correct 23% (02:05) wrong based on 1021 sessions HideShow timer Statistics 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

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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, 12:02 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

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.

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17 Jun 2017, 09:10
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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.

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

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17 Jun 2017, 09:22
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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 15 Nov 2017, 15:57 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

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.

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Re: Kevin invested $8,000 for one year at a simple annual interest rate of [#permalink] Show Tags 20 Nov 2017, 16:58 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...

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04 Jul 2018, 21:10
($$\frac{6}{100}$$)(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 Answer E. SVP Joined: 18 Aug 2017 Posts: 1792 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: Kevin invested$8,000 for one year at a simple annual interest rate of  [#permalink]

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19 Jan 2019, 01:37
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 _________________ If you liked my solution then please give Kudos. Kudos encourage active discussions. Re: Kevin invested$8,000 for one year at a simple annual interest rate of   [#permalink] 19 Jan 2019, 01:37
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