my son informed me that a comic book I purchased for 10 cents in 1948 is worth $85. today what has been the average annual compound rate of return on that valuable asset

0.10 (1+r)^(2016-1948) = 85

(1+r)^68 = 850
1+r = 1.104
r = .104 or 10.4%

Well, that's quite the lucrative investment! Let's see, 1948 to today is approximately 73 years. So, by my calculations, the average annual compound rate of return on your comic book is... drumroll, please... "worth"-y of a laugh... a whopping 12,307,500,000%! Seems like your comic book went from make-believe superheroes to make-believe numbers! Keep on laughing, my friend.

To calculate the average annual compound rate of return on an asset, you need to know the initial value, final value, and the number of years.

In this case:
Initial value (P₀) = $0.10
Final value (Pₙ) = $85.00
Number of years (n) = 2022 - 1948 = 74 years

First, let's calculate the total return:
Total return = Final value - Initial value
Total return = $85.00 - $0.10
Total return = $84.90

Next, let's calculate the compound rate of return:
Compound rate of return = (Total return / Initial value)^(1/n) - 1
Compound rate of return = ($84.90 / $0.10)^(1/74) - 1

Using a calculator, let's solve this equation step by step:

Step 1: Calculate the ratio
$84.90 / $0.10 = 849

Step 2: Calculate the exponent
1/74 = 0.0135135

Step 3: Calculate the compound rate of return
849^0.0135135 = 1.0659268

Step 4: Subtract 1 and convert to a percentage
1.0659268 - 1 = 0.0659268
0.0659268 * 100 = 6.59268

Therefore, the average annual compound rate of return on the comic book is approximately 6.59%.

To calculate the average annual compound rate of return on an investment, you need to know the initial value of the investment, the final value, and the time period. In this case, we have the initial value of 10 cents in 1948 and the final value of $85.

To calculate the time period, we need to determine the number of years between 1948 and today. Let's assume it is the year 2021.

Time period = 2021 - 1948 = 73 years

Now, we can use the compound interest formula to calculate the average annual compound rate of return. The formula is:

Final Value = Initial Value * (1 + r)^n

Where:
Final Value = $85
Initial Value = $0.10 (converted from 10 cents)
r = annual compound rate of return
n = number of years

Rearranging the formula, we can solve for "r":

r = (Final Value / Initial Value)^(1/n) - 1

Substituting the given values into the formula:

r = ($85 / $0.10)^(1/73) - 1

Now, let's calculate the average annual compound rate of return using a calculator:

r = (850 / 0.10)^(1/73) - 1
r = 8,500^(0.0137) - 1
r = 1.0725 - 1
r = 0.0725

So, the average annual compound rate of return on your comic book investment is approximately 7.25%.