## Answers

Ending value = beginning value * (1 + r)^{n},

where ending value = value in 2014

beginning value = value in 1925. This is $1 for all the investments.

r = geometric average annual return.

n = number of years from 1925 to 2014, which is 89 years.

**(a)**

$27,419.32 = $1 * (1 + r)^{89}

r = ($27,419.32 / $1)^{1/89} - 1

r = 12.17%.

**(b)**

$5,316.85 = $1 * (1 + r)^{89}

r = ($5,316.85 / $1)^{1/89} - 1

r = 10.12%.

**(c)**

$135.18 = $1 * (1 + r)^{89}

r = ($135.18 / $1)^{1/89} - 1

r = 5.67%.

**(d)**

$20.58 = $1 * (1 + r)^{89}

r = ($20.58 / $1)^{1/89} - 1

r = 3.46%.

**(e)**

$13.10 = $1 * (1 + r)^{89}

r = ($13.10 / $1)^{1/89} - 1

r = 2.93%.

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