You deposit $3600 each quarter into an account earning 4% interest compounded quarterly.

(a) How much will you have in the account in 14 years? $

To solve this problem, we use the formula for the future value of an annuity compounded periodically:

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

Where:
- $ A $ is the future value of the annuity.
- $ P $ is the periodic deposit amount.
- $ r $ is the annual interest rate (expressed as a decimal).
- $ n $ is the number of times the interest is compounded per year.
- $ t $ is the number of years.

Given:
- $ P = 3600 $ (quarterly deposit),
- $ r = 4\% = 0.04 $,
- $ n = 4 $ (compounded quarterly),
- $ t = 14 $ years.

Let's compute the future value.

\[
A = 3600 \left( \frac{(1 + 0.04/4)^{4 \times 14} - 1}{0.04/4} \right)
\] 

Now I’ll calculate this.The amount you will have in the account after 14 years is approximately **$268,491.53**.

Would you like further details or have any questions?

Here are 5 related questions for deeper understanding:
1. What happens if you increase the interest rate to 5%?
2. How would the future value change if deposits are made monthly instead of quarterly?
3. What is the total amount of interest earned over the 14 years?
4. How long would it take to reach $300,000 with the same deposit and interest rate?
5. How would the final amount be affected if the interest were compounded annually instead of quarterly?

**Tip:** The more frequently interest is compounded, the greater the future value due to the effect of compounding.

You deposit $3600 each quarter into an account earning 4% interest compounded quarterly. (a) How much will you have in the account in 14 years?

Learn how to calculate the future value of $3600 deposited quarterly into an account with 4% interest compounded quarterly over 14 years. This detailed solution covers key financial concepts, including the future value of an annuity formula, and is suitable for high school and college-level students.

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