To find the value of $100 invested at 8% interest compounded continuously after 15 years, we can use the formula for continuous compounding:
A(t) = Pert
Where:
A(t) is the amount of money accumulated after t years,
P is the principal amount (initial investment),
e is the base of the natural logarithm (approximately 2.71828),
r is the annual interest rate (as a decimal),
t is the time the money is invested for.
Given:
P = $100 (initial investment)
r = 0.08 (8% interest rate as a decimal)
t = 15 years
Substitute these values into the formula:
A(15) = 100 * e^(0.08*15)
Now, calculate the value:
A(15) = 100 * e^(1.2)
Using a calculator, you can find the value of e^(1.2) which is approximately 3.320117485.
Finally, multiply the initial investment by the calculated value:
A(15) = 100 * 3.320117485 ≈ $332.01
Therefore, $100 invested at 8% interest compounded continuously would be worth approximately $332.01 after 15 years.
