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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