Question

a bank offers an investment account with an annual interest rate of 1.34% compounded annually. scott invests $4300 into the account for 3 years.

answer the questions below. do not round any intermediate computations, and round your final answers to the nearest cent. if necessary, refer to the list of financial formulas.

(a) assuming no withdrawals are made, how much money is in scotts account after 3 years?
$

(b) how much interest is earned on scotts investment after 3 years?
$

Explanation:

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</pre_analysis>

<reasoning>

Identify given parameters

\[

$$\begin{aligned} P &= 4300 \\ r &= 0.0134 \\ t &= 3 \\ n &= 1 \end{aligned}$$

\]

Calculate future value

\[

$$\begin{aligned} A &= P(1 + r)^t \\ A &= 4300(1 + 0.0134)^3 \\ A &= 4300(1.0134)^3 \\ A &\approx 4300(1.040742) \\ A &\approx 4475.1925 \\ A &\approx 4475.19 \end{aligned}$$

\]

Calculate interest earned

\[

$$\begin{aligned} I &= A - P \\ I &= 4475.1925 - 4300 \\ I &\approx 175.1925 \\ I &\approx 175.19 \end{aligned}$$

\]
</reasoning>

<answer>

Question 1

(a) Assuming no withdrawals are made, how much money is in Scott's account after 3 years?
$4475.19

Question 2

(b) How much interest is earned on Scott's investment after 3 years?
$175.19
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multi-part",
"knowledge_point": [
"Mathematics",
"Algebra",
"Compound Interest"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 2,
"skills_matched": [
"step_cot",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Compound Interest",
"Future Value"
],
"new_concepts": [],
"current_concepts": [
"Compound Interest",
"Future Value"
]
}
</pre_analysis>

<reasoning>

Identify given parameters

\[

$$\begin{aligned} P &= 4300 \\ r &= 0.0134 \\ t &= 3 \\ n &= 1 \end{aligned}$$

\]

Calculate future value

\[

$$\begin{aligned} A &= P(1 + r)^t \\ A &= 4300(1 + 0.0134)^3 \\ A &= 4300(1.0134)^3 \\ A &\approx 4300(1.040742) \\ A &\approx 4475.1925 \\ A &\approx 4475.19 \end{aligned}$$

\]

Calculate interest earned

\[

$$\begin{aligned} I &= A - P \\ I &= 4475.1925 - 4300 \\ I &\approx 175.1925 \\ I &\approx 175.19 \end{aligned}$$

\]
</reasoning>

<answer>

Question 1

(a) Assuming no withdrawals are made, how much money is in Scott's account after 3 years?
$4475.19

Question 2

(b) How much interest is earned on Scott's investment after 3 years?
$175.19
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multi-part",
"knowledge_point": [
"Mathematics",
"Algebra",
"Compound Interest"
]
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