A young graduate looks to save money to buy a house 7.00 years from today. He is somewhat conservative and will invest his money in a bond fund that pays 5.00% APR with quarterly compounding. The graduate invests $11,920.00 today. How much will his account be worth in 7.00 years?

To calculate how much the graduate's account will be worth in 7 years, we can use the formula for compound interest:

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

Where:
- $A$ is the amount of money in the account after interest.
- $P$ is the initial investment (\$11,920).
- $r$ is the annual interest rate (5.00% or 0.05 as a decimal).
- $n$ is the number of times the interest is compounded per year (quarterly compounding means $n = 4$).
- $t$ is the number of years the money is invested (7.00 years).

### Step-by-Step Calculation:
\[
A = 11920 \left(1 + \frac{0.05}{4}\right)^{4 \times 7}
\]

Let's compute this now.

The graduate's account will be worth approximately **$16,878.63** after 7 years.

Would you like more details or have any questions?

Here are five related questions to explore:

1. What if the interest rate were 6.00% instead of 5.00%?
2. How would the value change if the investment period were 10 years instead of 7 years?
3. How does quarterly compounding compare with annual compounding over the same period?
4. What is the formula for continuous compounding, and how much would the account be worth under it?
5. How much would the graduate need to invest today to reach $20,000 in 7 years at this interest rate?

**Tip:** The more frequently interest is compounded, the more money accumulates in the account over time.

Learn how to calculate compound interest for a 7-year investment with a 5.00% APR and quarterly compounding. This example shows how an initial investment of $11,920 will grow to approximately $16,878.63 using the compound interest formula. Explore key financial concepts and the impact of compounding over time.

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