5

Set 4: Exponential Functions (Advanced)

Explanation

Answer: A

$30,000 is invested at 7.2% annual interest compounded monthly. How much interest is earned in the first year?

A.

$2,235.09

✓ Correct
B.

$2,160.00

C.

$2,300.00

D.

$2,500.00

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Calculate the interest earned. 1. Values: P=30000P = 30000, r=0.072r = 0.072, n=12n = 12, t=1t = 1. 2. Final Amount: A=30000(1+0.07212)12=30000(1.006)12A = 30000(1 + \frac{0.072}{12})^{12} = 30000(1.006)^{12}. 3. Calculate: (1.006)121.0745(1.006)^{12} \approx 1.0745, so A32,235A \approx 32,235. 4. Interest: 32,23530,000=2,23532,235 - 30,000 = 2,235. Strategic Tip: Interest earned = Final amount - Principal. Choice B is incorrect because this uses simple interest, not compound. Choice C is incorrect because the calculation is wrong. Choice D is incorrect because this is too high.

Key Steps:

The correct answer is $2,235.09

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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