A bank features a savings account that has an annual percentage rate of 5.9 % with interest compounded monthly. Sadiqa deposits $11,000 into the account.

How much money will Sadiqa have in the account in 1 year?
Answer = $ .  *Round answer to the nearest penny.*

What is the annual percentage yield (APY) for the savings account?
APY= %. *Round to the nearest hundredth of a percent.*

### Step 1: Calculate the amount in the account after 1 year

The formula to calculate the future value of an investment compounded monthly is:

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

Where:
- $A$ = future value of the investment (what we're solving for)
- $P$ = principal amount (initial deposit) = 11,000
- $r$ = annual interest rate (decimal) = 5.9% = 0.059
- $n$ = number of times interest is compounded per year = 12 (monthly compounding)
- $t$ = number of years = 1

Now, substituting the values:

\[
A = 11,000 \left(1 + \frac{0.059}{12}\right)^{12 \times 1}
\]

First, calculate the monthly interest rate:

\[
\frac{0.059}{12} = 0.0049167
\]

Now:

\[
A = 11,000 \left(1 + 0.0049167\right)^{12}
\]
\[
A = 11,000 \left(1.0049167\right)^{12}
\]
\[
A = 11,000 \times 1.060746
\]
\[
A \approx 11,668.21
\]

Thus, after 1 year, Sadiqa will have **$11,668.21** in the account.

---

### Step 2: Calculate the Annual Percentage Yield (APY)

The APY can be calculated using the formula:

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

Where:
- $r = 0.059$
- $n = 12$

Substituting the values:

\[
APY = \left(1 + \frac{0.059}{12}\right)^{12} - 1
\]
\[
APY = \left(1 + 0.0049167\right)^{12} - 1
\]
\[
APY = 1.060746 - 1
\]
\[
APY = 0.060746
\]

To express this as a percentage:

\[
APY = 6.07\%
\]

Thus, the **Annual Percentage Yield (APY) is 6.07%**.

---

### Final Answers:
- **Amount after 1 year**: **$11,668.21**
- **APY**: **6.07%**

Do you want more details or have any questions?

---

Here are 5 related questions for further exploration:
1. What would the balance be after 5 years under the same conditions?
2. How would the balance change if the interest were compounded daily instead of monthly?
3. What would the APY be if the interest rate were 7% instead of 5.9%?
4. How does APY differ from APR, and why is it higher?
5. What would be the effect of doubling the initial deposit to $22,000?

**Tip**: The APY takes into account the effect of compounding, which is why it is slightly higher than the nominal interest rate.

A bank features a savings account that has an annual percentage rate of 5.9% with interest compounded monthly. Sadiqa deposits $11,000 into the account.

How much money will Sadiqa have in the account in 1 year?

What is the annual percentage yield (APY) for the savings account?

Learn how to calculate the future value of a $11,000 deposit with a 5.9% APR compounded monthly. This guide also covers how to compute the APY, providing step-by-step explanations for both formulas. Suitable for high school students in Grades 10-12.

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