If she deposits $10,000 at 1.85% interest, compounded continuously, what would her ending balance be after three years?  

The formula for continuously compounded interest is:

\[
A = P \cdot e^{rt}
\]

Where:
- $ A $ is the ending balance (future value),
- $ P $ is the principal amount (initial deposit),
- $ r $ is the interest rate (expressed as a decimal),
- $ t $ is the time (in years),
- $ e $ is the mathematical constant approximately equal to 2.71828.

In this case:
- $ P = 10,000 $,
- $ r = 1.85\% = 0.0185 $,
- $ t = 3 \text{ years} $.

Now let's calculate the ending balance:

\[
A = 10,000 \cdot e^{0.0185 \cdot 3}
\]

I’ll compute this.The ending balance after three years with a continuously compounded interest of 1.85% would be approximately \$10,570.69.

Would you like any further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would the ending balance change if the interest rate were higher or lower?
2. What is the effect of compounding interest continuously versus annually or quarterly?
3. How does the formula for continuously compounded interest differ from simple interest?
4. What would the balance be if she left the money for 5 years instead of 3?
5. How can this formula be rearranged to find the interest rate given a future balance?

**Tip:** Continuously compounded interest grows faster than interest compounded annually because it's calculated and added to the balance at every moment.

If she deposits $10,000 at 1.85% interest, compounded continuously, what would her ending balance be after three years?

Learn how to calculate the ending balance of a $10,000 deposit at 1.85% interest, compounded continuously over 3 years. This problem involves the formula for continuously compounded interest (A = P * e^(rt)) and covers exponential growth concepts. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation