Suppose the Winner of a $4,000,000 Sweepstakes Will Be Paid $\sum _ { n = 1 } ^ { 40 } 100,000 \left( \frac { 1 } { 1.05 } \right) ^ { n }$

question 172

Multiple Choice

Suppose the winner of a $4,000,000 sweepstakes will be paid $100,000 per year for 40 years, starting a year from now. The money earns 5% interest per year. The present value of the winnings is $\sum _ { n = 1 } ^ { 40 } 100,000 \left( \frac { 1 } { 1.05 } \right) ^ { n }$ . Compute the present value using the formula for the $n$ th partial sum of a geometric series. Round your answer to two decimal places.

• A) \(\$ 6,852,274.09\)
• B) \(\$ 1,959,646.05\)
• C) \(\$ 4,568,182.73\)
• D) \(\$ 1,246,221.03\)
• E) \(\$ 1,715,908.64\)

Understand the economic impact of agriculture policy on production and consumption.

Analyze the effects of agricultural subsidies and price supports on farmers and taxpayers.

Distinguish between different agricultural support programs and their implications on market outcomes.

Evaluate the role of government in addressing agricultural surpluses and shortages through policy measures.

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Definitions:

Factoring

The process of breaking down an equation or number into its constituent parts, or 'factors', that multiply together to form the original number or equation.

Equation

A declaration in the field of mathematics that two expressions possess equal value.

Factoring

A mathematical process of breaking down an expression into simpler components that, when multiplied together, produce the original expression.

Equation

A mathematical statement that asserts the equality of two expressions, typically formatted as 'expression = expression'.