Question

example 3: present value for simple interest

if you can earn 6% interest, what lump sum must be deposited now so that its value will be $3500 after 9 months?

Explanation:

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<reasoning>

Identify given parameters

\[

$$\begin{aligned} A &= 3500 \\ r &= 0.06 \\ t &= \frac{9}{12} = 0.75 \end{aligned}$$

\]

Apply present value formula

\[

$$\begin{aligned} P &= \frac{A}{1 + rt} \\ P &= \frac{3500}{1 + 0.06 \times 0.75} \end{aligned}$$

\]

Calculate principal amount

\[

$$\begin{aligned} P &= \frac{3500}{1 + 0.045} \\ P &= \frac{3500}{1.045} \\ P &\approx 3349.28 \end{aligned}$$

\]
</reasoning>

<answer>
\(P \approx \$3349.28\)
</answer>

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"question_type": "Free Response",
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"Mathematics",
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Answer:

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</pre_analysis>

<reasoning>

Identify given parameters

\[

$$\begin{aligned} A &= 3500 \\ r &= 0.06 \\ t &= \frac{9}{12} = 0.75 \end{aligned}$$

\]

Apply present value formula

\[

$$\begin{aligned} P &= \frac{A}{1 + rt} \\ P &= \frac{3500}{1 + 0.06 \times 0.75} \end{aligned}$$

\]

Calculate principal amount

\[

$$\begin{aligned} P &= \frac{3500}{1 + 0.045} \\ P &= \frac{3500}{1.045} \\ P &\approx 3349.28 \end{aligned}$$

\]
</reasoning>

<answer>
\(P \approx \$3349.28\)
</answer>

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"Mathematics",
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"Simple Interest"
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