John Wins the Lottery and Has the Following Three Payout

question 84

Multiple Choice

John wins the lottery and has the following three payout options for after-tax prize money: 1. $150,000 per year at the end of each of the next six years
2) $300,000 (lump sum) now
3) $500,000 (lump sum) six years from now
The required rate of return is 9%. What is the present value if he selects the first option? Round to nearest whole dollar.
Present value of annuity of $1:
$$\begin{array} { | r | r | r | r | } \hline & { 8 \% } & { 9 \% } &{ 10 \% } \\\hline 1 & 0.926 & 0.917 & 0.909 \\\hline 2 & 1.783 & 1.759 & 1.736 \\\hline 3 & 2.577 & 2.531 & 2.487 \\\hline 4 & 3.312 & 3.24 & 3.17 \\\hline 5 & 3.993 & 3.89 & 3.791 \\\hline 6 & 4.623 & 4.486 & 4.355 \\\hline 7 & 5.206 & 5.033 & 4.868 \\\hline\end{array}$$ Present value of $1:
$$\begin{array} { | l | r | r | r | } \hline &{ 8 \% } &{ 9 \% } & 10 \% \\\hline 1 & 0.926 & 0.917 & 0.909 \\\hline 2 & 0.857 & 0.842 & 0.826 \\\hline 3 & 0.794 & 0.772 & 0.751 \\\hline 4 & 0.735 & 0.708 & 0.683 \\\hline 5 & 0.681 & 0.65 & 0.621 \\\hline 6 & 0.63 & 0.596 & 0.564 \\\hline 7 & 0.583 & 0.547 & 0.513 \\\hline\end{array}$$

• A) $750,000
• B) $672,900
• C) $450,000
• D) $450,050

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Definitions:

Compound Annual Rate

The rate at which an investment grows annually when interest is reinvested to earn additional interest.

Nominal Rate

The interest rate before adjustments for inflation or other factors, often referred to as the stated or face interest rate.

Compounded Quarterly

A method of calculating interest where the accrued interest is added to the principal sum every quarter, thus increasing the base for the next interest calculation.

Nominal Rate

The quoted interest rate on a loan or investment, not adjusting for the effect of compounding or inflation.