 the appropriate compound interest formula to compute the balance in the account after the stated period of time
​$13 comma 000 is invested for 5 years with an APR of 5​% and quarterly compounding.
Question content area bottom
Part 1
The balance in the account after 5 years is ​$
  
enter your response here.
​(Round to the nearest cent as​ needed.)

To calculate the balance in the account using compound interest with quarterly compounding, the appropriate formula is:

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

Where:
- $ A $ is the future value (the balance in the account after time $ t $),
- $ P $ is the principal amount (initial investment),
- $ r $ is the annual interest rate (as a decimal),
- $ n $ is the number of times the interest is compounded per year,
- $ t $ is the number of years.

In your case:
- $ P = 13,000 $ (the initial investment),
- $ r = 0.05 $ (5% APR, as a decimal),
- $ n = 4 $ (since the interest is compounded quarterly),
- $ t = 5 $ years.

Now, we can calculate the balance.

\[
A = 13,000 \left(1 + \frac{0.05}{4}\right)^{4 \times 5}
\]

Let me calculate that for you.The balance in the account after 5 years will be \$16,666.48, rounded to the nearest cent.

Would you like more details or have any questions? 

Here are 5 related questions to explore:
1. What happens if the compounding is done monthly instead of quarterly?
2. How would the balance change if the APR increased to 6%?
3. What is the effect of doubling the investment period to 10 years?
4. How does continuous compounding compare to quarterly compounding?
5. Can the compound interest formula be rearranged to solve for the interest rate?

**Tip**: Compounding more frequently results in a higher final amount since interest is calculated and added more often.

The appropriate compound interest formula to compute the balance in the account after the stated period of time: $13,000 is invested for 5 years with an APR of 5% and quarterly compounding. The balance in the account after 5 years is ​$ (Round to the nearest cent as​ needed).

Calculate the balance after investing $13,000 for 5 years at a 5% annual percentage rate (APR) with quarterly compounding. Learn how the compound interest formula A = P(1 + r/n)^(nt) applies to this situation. Final balance rounded to the nearest cent.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation