question 18

suppose $30,000 is deposited into an account paying 4.5% interest, compounded continuously.

how much money is in the account after 8 years if no withdrawals or additional deposits are made?

$41,920.34
$42,866.59
$42,999.88
$41,788.24

Question

question 18

suppose $30,000 is deposited into an account paying 4.5% interest, compounded continuously.

how much money is in the account after 8 years if no withdrawals or additional deposits are made?

$41,920.34
$42,866.59
$42,999.88
$41,788.24

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Continuous Compounding" ], "new_concepts": [], "current_concepts": [ "Continuous Compounding" ] } ## Identify the given values and formula Using the *Continuous Compounding* knowledge point $$ \begin{aligned} P &= 30000 \ r &= 0.045 \ t &= 8 \ A &= P e^{r t} \end{aligned} $$ ## Substitute the values into the formula Using the *Continuous Compounding* knowledge point $$ \begin{aligned} A &= 30000 \cdot e^{0.045 \cdot 8} \ A &= 30000 \cdot e^{0.36} \end{aligned} $$ ## Calculate the final amount Using the *Continuous Compounding* knowledge point $$ \begin{aligned} e^{0.36} &\approx 1.4333294 \ A &\approx 30000 \cdot 1.4333294 \ A &\approx 42999.88 \end{aligned} $$

(A) $41,920.34

(B) $42,866.59

(C) $42,999.88

(D) $41,788.24

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Continuous Compounding" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given values and formula

Substitute the values into the formula

Calculate the final amount

Answer: