In the original example in section 1, $1,000 was invested at a 2% interest rate compounded n times per year. Even when n increased to 365 so the interest was compounded every day, the maximum value in the account after 1 year was less than $1020.21.
There is always a maximum amount of increase in an account from compound interest. That amount is referred to as the result of “continuous compounding.” When interest is compounded continuously, the formula is:
P = P 0ert
where the principal P 0, is invested in an account that pays an annual interest rate r (written as a decimal), compounded for t years.
The number e is an irrational constant (like the number π). It is the base of the “natural logarithm
A. Use the formula for continuous compounding with the original example: $1000 invested at 2% for 1 year. Record the amount to 5 decimal places. Use a calculator.
B. Compare it to the result using the original compound interest formula with n = 365 calculated to 5 decimal places. Which has a larger value? Explain.