Use the compound interest formula for compounding more than once a year to determine the accumulated balance after the stated period.
A ​$26 comma 000 deposit at an APR of 3.4​% with quarterly compounding for 34 years.
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Part 1
The amount after 34 years will be ​$
  
enter your response here.
​(Round to the nearest cent as​ needed.)

The compound interest formula for compounding more than once a year is:

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

Where:
- $ A $ is the accumulated amount (the future value),
- $ P $ is the principal (initial deposit),
- $ 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.

### Given:
- $ P = 26,000 $ dollars,
- $ r = 3.4\% = 0.034 $,
- $ n = 4 $ (since compounding is quarterly),
- $ t = 34 $ years.

Now, we can plug the values into the formula to find $ A $:

\[
A = 26,000 \left(1 + \frac{0.034}{4}\right)^{4 \times 34}
\]

Let's calculate that.The accumulated balance after 34 years, with quarterly compounding, will be approximately **$82,204.60**.

Would you like more details or have any questions?

Here are five related questions:
1. What is the formula for continuous compounding?
2. How would the result change with monthly compounding instead of quarterly?
3. What happens if the interest rate is compounded annually instead?
4. How does the length of the deposit period affect the accumulated balance?
5. How can inflation impact the real value of the accumulated balance?

**Tip:** The more frequently interest is compounded, the larger the accumulated amount will be over time, even if the annual interest rate stays the same.

Use the compound interest formula for compounding more than once a year to determine the accumulated balance after the stated period. A $26,000 deposit at an APR of 3.4% with quarterly compounding for 34 years. The amount after 34 years will be ​$ __ (Round to the nearest cent as needed.)

Calculate the accumulated balance for a $26,000 deposit at an APR of 3.4% with quarterly compounding over 34 years. Learn how to apply the compound interest formula to determine the future value with step-by-step instructions. Perfect for students in Grades 10-12 studying financial mathematics.

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