question 10

suppose \$28,000 is deposited into an account paying 5.25\% interest, which is compounded continuously.

how much money will be in the account after 4 years if no withdrawals or additional deposits are made?

\$34,542.99
\$36,721.16
\$32,748.23
\$30,904.77

Question

question 10

suppose \$28,000 is deposited into an account paying 5.25\% interest, which is compounded continuously.

how much money will be in the account after 4 years if no withdrawals or additional deposits are made?

\$34,542.99
\$36,721.16
\$32,748.23
\$30,904.77

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 $$ \begin{aligned} P &= 28000 \ r &= 5.25\% = 0.0525 \ t &= 4 \ A &= P e^{rt} \end{aligned} $$ ## Calculate the exponent Using the *Continuous Compounding* knowledge point $$ rt = 0.0525 \times 4 = 0.21 $$ ## Compute the final balance Using the *Continuous Compounding* knowledge point $$ \begin{aligned} A &= 28000 \times e^{0.21} \ e^{0.21} &\approx 1.233678 \ A &\approx 28000 \times 1.233678 \approx 34542.985 \end{aligned} $$ ## Round to the nearest cent Using the *Continuous Compounding* knowledge point $$ A \approx \$34,542.99 $$

(A) \$34,542.99

(B) \$36,721.16

(C) \$32,748.23

(D) \$30,904.77

{ "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

Calculate the exponent

Compute the final balance

Round to the nearest cent

Answer: