use the ordinary annuity formula shown to the right to determine the accumulated amount in the annuity if \$60 is invested semiannually for 15 years at 3.5\% compounded semiannually.

the accumulated amount will be \$\box.
(round to the nearest cent as needed.)

Question

use the ordinary annuity formula shown to the right to determine the accumulated amount in the annuity if \$60 is invested semiannually for 15 years at 3.5\% compounded semiannually.

the accumulated amount will be \$\box.
(round to the nearest cent as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Ordinary Annuity", "Future Value" ], "new_concepts": [], "current_concepts": [ "Ordinary Annuity", "Future Value" ] } ## Identify the given parameters $$ \begin{aligned} P &= 60 \ r &= 0.035 \ m &= 2 \ t &= 15 \ n &= m \times t = 30 \ i &= \frac{r}{m} = \frac{0.035}{2} = 0.0175 \end{aligned} $$ ## Apply the ordinary annuity formula $$ \begin{aligned} A &= P \times \frac{(1 + i)^n - 1}{i} \ A &= 60 \times \frac{(1 + 0.0175)^{30} - 1}{0.0175} \end{aligned} $$ ## Calculate the accumulated amount $$ \begin{aligned} (1.0175)^{30} &\approx 1.682015 \ A &\approx 60 \times \frac{1.682015 - 1}{0.0175} \ A &\approx 60 \times \frac{0.682015}{0.0175} \ A &\approx 60 \times 38.972286 \ A &\approx 2338.337 \end{aligned} $$ Use the ordinary annuity formula shown to the right to determine the accumulated amount in the annuity if $60 is invested semiannually for 15 years at 3.5% compounded semiannually. The accumulated amount will be $2338.34. (Round to the nearest cent as needed.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Ordinary Annuity" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given parameters

Apply the ordinary annuity formula

Calculate the accumulated amount

Answer: