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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 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

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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...

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

Total interest from both investments is 480 + 400 + 416 = 1296(Option E)

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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.

Answer: E.
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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
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Re: Kevin invested $8,000 for one year at a simple annual interest rate of [#permalink]

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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


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