find the present value for the following future amount.

$9890 at 4.5% compounded semiannually for 12 years

the present value is $
(do not round until the final answer. then round to the nearest cent as needed.)

Question

find the present value for the following future amount.

$9890 at 4.5% compounded semiannually for 12 years

the present value is $
(do not round until the final answer. then 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": [ "Present Value", "Compound Interest" ], "new_concepts": [], "current_concepts": [ "Present Value", "Compound Interest" ] } ## Identify the given parameters $$ \begin{aligned} &FV = 9890 \ &r = 0.045 \ &m = 2 \ &t = 12 \ &n = m \times t = 24 \ &i = \frac{r}{m} = \frac{0.045}{2} = 0.0225 \end{aligned} $$ ## Apply the present value formula $$ \begin{aligned} &PV = \frac{FV}{(1 + i)^n} \ &PV = \frac{9890}{(1 + 0.0225)^{24}} \end{aligned} $$ ## Calculate the final value $$ \begin{aligned} &PV = \frac{9890}{(1.0225)^{24}} \ &PV \approx \frac{9890}{1.7057666} \ &PV \approx 5797.9798 \end{aligned} $$ Find the present value for the following future amount. $9890 at 4.5% compounded semiannually for 12 years The present value is $5797.98 (Do not round until the final answer. Then round to the nearest cent as needed.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Present Value" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given parameters

Apply the present value formula

Calculate the final value

Answer: