Answer:
$1,342.64
Step-by-step explanation:
Interest is the amount that a balance increases over time.
Continuous Interest
Continuously compounded interest means that the interest is compounded an infinite amount of times within a given period. One mathematician studied continuously compounded interest. In his studies, he found the constant known as Euler's constant, which is represented by e. Euler's constant is approximately 2.7, but in reality, it is an irrational number. We can use this constant to find the balance after 10 years given a 4% interest rate.
Interest Formula
The formula for continuously compounded interest is [tex]A = Pe^{rt}[/tex]. In this formula, A is the total amount, P is the principal (the initial investment), r is the interest rate as a decimal, and t is the time in years. All we need to do is plug in the information we know and solve for A.
- [tex]A = 900*e^{0.04*10}[/tex]
- A = 1,342.64
This means that the balance after 10 years is $1,342.64.
