Problem Solving

AbeNeedsAnswers 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

E

Interest earned on $8000 for 1 year @ 6% = (8000 x 6 x 1)/100 = $480

Regarding the second sum $10000, we must calculate the interest twice since the compounding is semi-annual, i.e., twice in a year.

Interest earned on $10000 for the first 6 months (1/2 year) @ 8% = (10000 x 8 x 1/2)/100 = $400

The sum for the second 6 month would be $10000 + the interest earned in the first 6 months = $10000 + $400 = $10400

Thus,

Interest earned on $10400 for the second 6 months (1/2 year) @ 8% = (10400 x 8 x 1/2)/100 = $416

Total interest earned by Kevin = 480 + 400 + 416 = [spoiler]$1296[/spoiler]

The correct answer: E

Hope this helps!

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Hi AbeNeedsAnswers,

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: E

GMAT assassins aren't born, they're made,
Rich

AbeNeedsAnswers 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