Question

In 1683, Jacob Bernoulli was the first person to calculate interest based on continuous compounding. While this is a well-known fact, a much lesser-known fact is that he then deposited the equivalent of $565 into a Swiss bank at 3% nominal interest rate, compounded continuously. Yes, he did have to explain the continuous concept to the banker. This was not difficult since the banker was his brother, who also was a mathematical genius (as all Bernoullis were). Jacob left the money in the bank with the instruction that no money would ever be withdrawn from it by his estate, unless hell froze over. Since most scientists agree that hell has never frozen over, what is the current value of this bank account after 336 years of Jacob’s deposit.

Answer 1

Current value with continuous compounding = $565 x e^rt, where

r: Nominal interest rate = 3% (= 0.03)

t: Time in years = 336

Current value with continuous compounding = $565 x e^{(0.03 x 336)},

= $565 x e^10.08

= $565 x 23,860.9855

= $13,481,456.83