Question

Money in a savings account is compounded continuously over time, t, and is modeled by the function f(t)=1000e0.047t. what is the rate at which the balance grows?

Answer 1

Compounded continuously the balance grows at a continuous rate of 1.7%.

What is compound interest ?

• Compound interest is when you earn interest on both the money you've saved and the interest you earn.
• So let's say you invest $1,000 (your principal) and it earns 5 percent (interest rate or earnings) once a year (the compounding frequency).

The model used for continuous compounding is

 f(t) = Pe^(rt)

where P is the principal amount, and r is the interest rate being compounded. Assuming a typo in your given equation, you have

 f(t) = 1000·e^(0.017t)

Matching the various parts of the equation, we see that P = 1000 and r = 0.017 = 1.7%.

Therefore, the balance grows at a continuous rate of 1.7%.

Learn more about compound interest

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