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:
Calculate the number of days since Columbus sailed to America.
Calculate the total amount earned without investing.
Calculate the amount if invested in an index fund.
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
Total Amount Earned Without Investing: 193,947 days x $5,000/day = $969,735,000
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)
- 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.
- 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:
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%.