A bank features a savings account that has an annual percentage rate of 4.5 % with interest compounded monthly. Agustín deposits $11,000 into the account.

How much money will Agustín have in the account in 1 year?
What is the annual percentage yield (APY) for the savings account?

### 1. How much money will Agustín have in the account in 1 year?

The formula for compound interest is given by:

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

Where:
- $ A $ is the amount in the account after interest,
- $ P $ is the initial principal (\$11,000),
- $ r $ is the annual interest rate (4.5% or 0.045),
- $ n $ is the number of times interest is compounded per year (monthly, so $ n = 12 $),
- $ t $ is the time in years (1 year).

Substituting the values:

\[
A = 11,000 \left( 1 + \frac{0.045}{12} \right)^{12 \times 1}
\]

Now, let's calculate the result.

After 1 year, Agustín will have approximately \$11,505.34 in the account.

### 2. What is the Annual Percentage Yield (APY)?

The APY is the effective annual rate of return, taking into account the compounding of interest. The formula for APY is:

\[
\text{APY} = \left( 1 + \frac{r}{n} \right)^n - 1
\]

Substituting the known values:

\[
\text{APY} = \left( 1 + \frac{0.045}{12} \right)^{12} - 1
\]

Let's calculate the APY.The Annual Percentage Yield (APY) for the savings account is approximately **4.59%**.

Would you like more details or have any questions? Here are 5 related questions you might find interesting:

1. How does the compound interest formula change if the interest is compounded daily?
2. What would be the account balance after 5 years with monthly compounding?
3. How much more would Agustín earn with an APY of 5% instead of 4.59%?
4. What would the APY be if the interest were compounded quarterly instead of monthly?
5. How is APY different from APR in terms of savings and loans?

**Tip:** The more frequently interest is compounded, the higher the final amount due to the effect of compounding. Monthly compounding usually leads to higher yields than annual compounding.

A bank features a savings account that has an annual percentage rate of 4.5% with interest compounded monthly. Agustín deposits $11,000 into the account. How much money will Agustín have in the account in 1 year? What is the annual percentage yield (APY) for the savings account?

Learn how to calculate compound interest and the annual percentage yield (APY) for a savings account with a 4.5% APR compounded monthly. Agustín deposits $11,000, and this guide walks through the key formulas and concepts. Suitable for Grades 10-12.

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