My son informed me that a comic book I purchased for 10 cents in 1948 is worth $55 today. What has been the average annual compound rate of return on that valuable asset?
Pt = Po * (r + 1)^n.
Pt = principal after time t (62 yrs.),
Po = initial investment,
r = rate per compounding period expressed as a decimal.
n = the number of compounding periods.
55 = 0.10 * (r + 1)^62,
Divide both sides by 0.10 and Solve for r:
550 = (r + 1)^62
Take the log of both sides:
log550 = 62*log(r + 1),
divide both sides by 62:
log550 / 62 = log(r + 1),
0.04420 = log(r + 1),
10^0.04420 = r + 1,
1.107132 = r + 1,
0.107132 = r, or
r = 0.107132 = 10.7132 % = annual
percentage rate ( APR ) compounded
annually.
To calculate the average annual compound rate of return, you need the initial value and the final value of the asset, as well as the number of years between the two.
Initial value: $0.10
Final value: $55
Let's assume you purchased the comic book in 1948 and the current year is 2022, which means the number of years is 2022 - 1948 = 74.
To find the average annual compound rate of return, use the formula:
Compound annual growth rate (CAGR) = (Final Value / Initial Value)^(1/Number of Years) - 1
CAGR = ($55 / $0.10)^(1/74) - 1
Using a calculator or spreadsheet, the calculation would be:
CAGR = (550 / 0.10)^(1/74) - 1
CAGR ≈ 33.60 - 1
CAGR ≈ 32.60
Therefore, the average annual compound rate of return on your comic book investment is approximately 32.60%.
To calculate the average annual compound rate of return on the comic book, we need to use the formula for compound interest:
Future Value = Present Value * (1 + Rate)^Time
In this case, the Present Value (PV) would be 0.10 cents (the amount you purchased the comic book for), and the Future Value (FV) is $55 (the current worth of the comic book). The Time would be the number of years, which we can calculate by subtracting the current year (2022) from the year you purchased the comic book (1948).
Let's calculate the Time first:
Time = Current Year - Year of Purchase
Time = 2022 - 1948
Time = 74 years
Now, let's rearrange the formula to solve for the Rate:
Rate = (FV / PV)^(1/Time) - 1
Plugging in the values:
Rate = ($55 / $0.10)^(1/74) - 1
Calculating this expression will give you the average annual compound rate of return on your comic book.
Please note that the historical compound interest rate may not fully account for inflation or other market-specific factors, so this calculation is an approximation.