\$7,800 is placed in an account with an annual interest rate of 7.25\%. how much will be in the account after 24 years, to the nearest cent?

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Compound Interest Formula", "Exponential Growth" ], "current_concepts": [ "Compound Interest Formula", "Exponential Growth" ] } ## Identify the given values and formula $$ \begin{aligned} P &= 7800 \ r &= 0.0725 \ t &= 24 \ A &= P(1 + r)^t \end{aligned} $$ ## Substitute the values into the formula $$ \begin{aligned} A &= 7800(1 + 0.0725)^{24} \ A &= 7800(1.0725)^{24} \end{aligned} $$ ## Calculate the final amount $$ \begin{aligned} (1.0725)^{24} &\approx 5.3541238 \ A &\approx 7800 \times 5.3541238 \ A &\approx 41762.17 \end{aligned} $$ $41,762.17$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Compound Interest Formula" ] }

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Explanation:

Identify the given values and formula

Substitute the values into the formula

Calculate the final amount

Answer: