If you worked every single day and made $5000/day from the time Columbus sailed to America. How much money would you have if you put all of it in a savings account that returned 2% interest each year?
To answer this question, we need to break it down into a few steps:
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Calculate the number of days since Columbus sailed to America.
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Calculate the total amount earned without investing.
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Calculate the amount if invested in an index fund.
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Number of Days Since Columbus Sailed to America: Columbus sailed to America in 1492. Let’s assume today’s date is September 27, 2023.
From October 12, 1492 (the day Columbus arrived in America) to September 27, 2023, is:
2023 – 1492 = 531 years
To calculate the number of days: 531 years x 365 days/year = 193,815 days
However, we need to account for leap years. Every 4 years there’s a leap year, but years divisible by 100 are not leap years unless they’re also divisible by 400. So:
(531 / 4) – (5 (1500, 1700, 1800, 1900, 2100) – 1 (2000 is divisible by 400)) = 132 leap years
193,815 days + 132 days = 193,947 days
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Total Amount Earned Without Investing: 193,947 days x $5,000/day = $969,735,000
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Amount if Invested in an Savings Account:
To calculate the compound interest over this period, we’d use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times interest is compounded per year.
- t is the number of years.
However, since you’re adding $5,000 every day, this becomes a problem of calculating the future value of an annuity compounded daily.
Given:
- Daily contribution (PMT) = $5,000
- Number of days (t) = 193,947 days
- Daily rate (r) = 2% annual return / 365 = 0.00005479
Using the future value formula for an annuity compounded daily:
FV=PMT×((1+r)t−1r)
After performing the calculations, the future value (FV) of the investment with a 2% annual return compounded daily over 193,947 days with a daily contribution of $5,000 is: approximately $2.35 trillion.
This result demonstrates the incredible power of compound interest over long periods of time, even with a relatively modest annual return of 2%.
