question 2 (multiple choice worth 3 points)
(comparing types of interest mc)

a business owner invested \$7,000 in a treasury bond paying 4.3% compounded semiannually. after 30 years, the value of the bond will be \$25,084.20. if the business owners investment was compounded continuously instead of twice per year, what would be the difference in the account balance after 30 years?

\$345.31
\$318.22
\$286.74
\$228.59

Question

question 2 (multiple choice worth 3 points)
(comparing types of interest mc)

a business owner invested \$7,000 in a treasury bond paying 4.3% compounded semiannually. after 30 years, the value of the bond will be \$25,084.20. if the business owners investment was compounded continuously instead of twice per year, what would be the difference in the account balance after 30 years?

\$345.31
  \$318.22
  \$286.74
  \$228.59

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": [ "Compound Interest Formula", "Comparing Interest Types" ], "new_concepts": [ "Continuous Compound Interest" ], "current_concepts": [ "Compound Interest Formula", "Comparing Interest Types", "Continuous Compound Interest" ], "concept_mastery_cards": { "compound_interest_formula": "Mastered", "comparing_interest_types": "Mastered" } } ## Calculate continuous compound balance Using the *Compound Interest Formula* and *Comparing Interest Types* knowledge points $$ \begin{aligned} P &= 7000 \ r &= 0.043 \ t &= 30 \ A_{\text{continuous}} &= P e^{rt} \ A_{\text{continuous}} &= 7000 \cdot e^{0.043 \cdot 30} \ A_{\text{continuous}} &= 7000 \cdot e^{1.29} \ e^{1.29} &\approx 3.632793 \ A_{\text{continuous}} &\approx 7000 \cdot 3.632793 \approx 25429.55 \end{aligned} $$ ## Find the difference in balances Using the *Comparing Interest Types* knowledge point $$ \begin{aligned} A_{\text{semiannual}} &= 25084.20 \ \text{Difference} &= A_{\text{continuous}} - A_{\text{semiannual}} \ \text{Difference} &\approx 25429.55 - 25084.20 = 345.35 \end{aligned} $$ Comparing with the options, the closest value is \$345.31.

(A) $345.31

(B) $318.22

(C) $286.74

(D) $228.59

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

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QUESTION IMAGE

Question

Explanation:

Calculate continuous compound balance

Find the difference in balances

Answer: