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Set 13: Exponential Functions (Advanced)

Explanation

Answer: A

A savings bond earns 5% interest compounded daily for 1 year. With $1,000 invested, what is the approximate final value?

Use: A=P(1+rn)ntA = P(1 + \frac{r}{n})^{nt} with n=365n = 365

A.

$1,051.27

✓ Correct
B.

$1,050.00

C.

$1,052.50

D.

$1,100.00

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Use daily compounding. 1. Values: P=1000P = 1000, r=0.05r = 0.05, n=365n = 365, t=1t = 1. 2. Formula: A=1000(1+0.05365)365A = 1000(1 + \frac{0.05}{365})^{365}. 3. Calculate: (1+0.05365)3651.05127(1 + \frac{0.05}{365})^{365} \approx 1.05127, so A1051.27A \approx 1051.27. Strategic Tip: Daily compounding approaches continuous compounding (ere^r). Choice B is incorrect because this is annual compounding. Choice C is incorrect because this calculation is incorrect. Choice D is incorrect because this assumes 10% growth.

Key Steps:

The correct answer is $1,051.27

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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