17. From age 20 to 30 Jack invested $2,000 per year in his IRA, and never saved another penny in his life. From age 20 to 65, Jill invested $2,000 per year in her IRA. Who do you think will have more money when they reach retirement age of 65? (Show your work). Assume opportunity cost of capital is 10%.

Jill's investment has a higher (by far) ending value than Jack.

Explanation:

Giving the following information:

From age 20 to 30 Jack invested $2,000 per year in his IRA, and never saved another penny in his life. From age 20 to 65, Jill invested $2,000 per year in her IRA.

Jack:

We need to calculate the final value of the firsts 10 deposits. The ending value of the investment until he is 65.

First 10 deposits:

FV= {A*[(1+i)^n-1]}/i

A= annual deposit= 2,000

n=10

i= 0.10

FV= {2,000*[(1.10^10)-1]}/ 0.10= $31,874.83

Now, the 35 years:

FV= PV*(1+i)^n

FV= 31,874.83*1.10^35= $895,760.40

Jill:

We need to calculate the final value of 45 deposits of $2,000:

FV= {A*[(1+i)^n-1]}/i

A= annual deposit= 2,000

i= 0.10

n= 45

FV= {2,000*[(1.10^45)-1]}/0.10= 1,437,809.67

Jill's investment has a higher (by far) ending value than Jack.

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