the winner of a lottery chooses to receive annual payments of \$170,000 at the end of each year for 25 years. if the current interest rate is 5.6\%, find the ... payments. (round your answer to the nearest cent. see example 5 in this section.)

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Present Value of Ordinary Annuity" ], "new_concepts": [], "current_concepts": [ "Present Value of Ordinary Annuity" ] } ## Identify the given parameters Using the *Present Value of Ordinary Annuity* knowledge point $$ \begin{aligned} &\text{Payment } (PMT) = \$170,000 \ &\text{Interest rate } (i) = 5.6\% = 0.056 \ &\text{Number of periods } (n) = 25 \text{ years} \end{aligned} $$ ## Calculate the present value Using the *Present Value of Ordinary Annuity* knowledge point $$ \begin{aligned} PV &= PMT \times \frac{1 - (1 + i)^{-n}}{i} \ PV &= 170,000 \times \frac{1 - (1 + 0.056)^{-25}}{0.056} \ PV &= 170,000 \times \frac{1 - (1.056)^{-25}}{0.056} \ PV &\approx 170,000 \times \frac{1 - 0.2562912}{0.056} \ PV &\approx 170,000 \times \frac{0.7437088}{0.056} \ PV &\approx 170,000 \times 13.280514 \ PV &\approx 2,257,687.43 \end{aligned} $$ $2,257,687.43$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Present Value of Ordinary Annuity" ] }

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Identify the given parameters

Calculate the present value

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