In the formula A(t) = Pert for continuously compound interest, the letters P, r, and t stand for , , and , respectively, and A(t) stands for . So if $100 is invested at an interest rate of 6% compounded continuously, then the amount after 4 years is

In the formula A(t) = Pert for continuously compounded interest:

• P stands for the principal amount (the initial amount of money)
• r stands for the annual interest rate (in decimal form)
• t stands for the time the money is invested for (in years)
• A(t) stands for the amount of money accumulated after n years, including interest.

So, if $100 is invested at an interest rate of 6% compounded continuously, then the amount after 4 years is calculated as follows:

First, convert the interest rate from a percentage to a decimal by dividing by 100: 6/100 = 0.06.

Then, substitute P = 100, r = 0.06, and t = 4 into the formula:

A(t) = Pert A(4) = 100 * e^(0.06*4) A(4) = 100 * e^0.24

Using the approximation e^0.24 ≈ 1.27125 (since the value of e, the base of the natural logarithm, is approximately 2.71828),

A(4) = 100 * 1.27125 A(4) = $127.13

So, the amount after 4 years is approximately $127.13.