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Here is a small part of a data set that describes Major League Baseball players as of opening day of the 2009 season:

 Player  Team  Position  Age  Height  Weight  Salary  Rodriguez,  Yankees  Infielder 336323033,000,000 Alex  Ramirez,  Dodgers  Outfielder 366020023,854,494 Manny  Santana,  Mets  Pitcher 306021018,876,139 Johan  Zambrano,  Cubs  Pitcher 276525518,750,000 Carlos  Suzuki,  Mariners  Outfielder 3551117018,000,000 Ichiro \begin{array}{lllccc} \text { Player } & \text { Team } & \text { Position } & \text { Age } & \text { Height } & \text { Weight } & \text { Salary } \\ \hline \text { Rodriguez, } & \text { Yankees } & \text { Infielder } & 33 & 6-3 & 230 & 33,000,000 \\ \text { Alex } & & & & & & \\ \text { Ramirez, } & \text { Dodgers } & \text { Outfielder } & 36 & 6-0 & 200 & 23,854,494 \\ \text { Manny } & & & & & & \\ \text { Santana, } & \text { Mets } & \text { Pitcher } & 30 & 6-0 & 210 & 18,876,139 \\ \text { Johan } & & & & & & \\ \text { Zambrano, } & \text { Cubs } & \text { Pitcher } & 27 & 6-5 & 255 & 18,750,000 \\ \text { Carlos } & & & & & & \\ \text { Suzuki, } & \text { Mariners } & \text { Outfielder } & 35 & 5-11 & 170 & 18,000,000 \\ \text { Ichiro } & & & & & & \\ \hline \end{array}

What do you think are the units of measurement for each of the quantitative variables?

Question

Barry learned in an online investment course that he should start investing as soon as possible. He had always thought that it would be smart to start investing after he finishes college and when his salary is high enough to pay the bills and to have money left over. He projects that will be 5105-10 years from now. Barry wants to compare the difference between investing now and investing later. A financial advisor who spoke to Barry suggested that a Roth IRA (Individual Retirement Account) would be a good investment for him to start. (Note: When table values do not include the information you need, use the formula FV=$1(1+R)NF V=\$ 1(1+R)^N where RR is the period rate and NN is the number of periods.)

If Barry purchases a $2,000\$ 2,000 Roth IRA when he is 2525 years old and expects to earn an average of 6%6 \% per year compounded annually over 3535 years (until he is 6060), how much will accumulate in the investment?

Solution

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We first solve for unknown variables using the given.

Interest Periods=Number of Years×Number of Interests Period per Year=35(1)=35\begin{aligned} \text{Interest Periods} &=\text{Number of Years} \times \text{Number of Interests Period per Year}\\ &=35(1)\\ &=35 \end{aligned}

Periodic Interest Rate=Annual Interest RateNumber of Interests Period per Year =6%1=6%\begin{aligned} \text{Periodic Interest Rate} &=\frac{\text{Annual Interest Rate}}{\text{Number of Interests Period per Year}} \\\ & =\frac{6\%}{1}\\ &=6\% \end{aligned}

Using the formula FV=$1(1+R)NFV = \$1 (1+ R)^N, we identify the future value of $1.00

FV=$1(1+.06)35=7.686086792\begin{aligned} FV= \$1 (1+ .06)^{35}=7.686086792 \end{aligned}

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