To help pay for new costumes for a​ play, a theater invests ​$
1700 in an 18​-month CD paying 4.4​% interest compounded monthly. Determine the amount the theater will receive when it cashes in the CD after 18 months.

To calculate the amount the theater will receive when it cashes in the CD after 18 months, we can use the formula for compound interest:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the amount of money accumulated after $ t $ years, including interest.
- $ P $ is the principal amount (the initial investment).
- $ r $ is the annual interest rate (decimal).
- $ n $ is the number of times the interest is compounded per year.
- $ t $ is the time the money is invested for in years.

### Given:
- $ P = 1700 $ (the initial investment),
- $ r = 4.4\% = 0.044 $ (annual interest rate),
- $ n = 12 $ (compounded monthly),
- $ t = \frac{18}{12} = 1.5 $ years (18 months converted to years).

Now, let's calculate the amount $ A $.The theater will receive approximately **$1,815.77** when it cashes in the CD after 18 months.

Would you like more details on the calculation or have any other questions?

Here are some related questions you might find useful:
1. How would the final amount change if the interest were compounded quarterly instead of monthly?
2. What if the interest rate were 5% instead of 4.4%?
3. How would the result differ if the CD were cashed out after 12 months?
4. What is the difference between simple interest and compound interest in this scenario?
5. What if the theater invested $2,500 instead of $1,700?

**Tip:** Always check how frequently the interest is compounded when dealing with investments, as it significantly impacts the final amount.

Learn how to calculate compound interest on a $1700 investment over 18 months with a 4.4% interest rate compounded monthly. Get the final amount the theater will receive after cashing in the CD.

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