A bank features a savings account that has an annual percentage rate of 3.6 % with interest compounded annually. Kelsi deposits $10,500 into the account.

How much money will Kelsi 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?
A
P
Y
=
 %. Round to the nearest hundredth of a percent.

Let's solve these questions step by step.

### 1. Amount in the Account After 1 Year

The formula for calculating the amount in the account with compound interest is:

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

Where:
- $A$ is the amount in the account after $t$ years
- $P$ is the principal amount (initial deposit)
- $r$ is the annual interest rate (decimal)
- $n$ is the number of times interest is compounded per year
- $t$ is the time the money is invested for in years

Given:
- $P = 10,500$
- $r = 3.6\%$ or 0.036
- $n = 1$ (compounded annually)
- $t = 1$ year

Substituting these values:

\[
A = 10,500 \left(1 + \frac{0.036}{1}\right)^{1 \times 1}
\]

\[
A = 10,500 \left(1 + 0.036\right)
\]

\[
A = 10,500 \times 1.036
\]

\[
A = 10,878
\]

Thus, Kelsi will have **$10,878.00** in the account after 1 year.

### 2. Calculating the Annual Percentage Yield (APY)

The APY formula is:

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

Plugging in the values:

\[
\text{APY} = \left(1 + \frac{0.036}{1}\right)^1 - 1
\]

\[
\text{APY} = 1.036 - 1
\]

\[
\text{APY} = 0.036
\]

Converting to a percentage:

\[
\text{APY} = 3.6\%
\]

So, the annual percentage yield (APY) is **3.60%**.

### Summary:
- Amount after 1 year: **$10,878.00**
- APY: **3.60%**

Would you like a detailed explanation or have any further questions?

#### Related Questions:
1. What would be the balance after 5 years with the same conditions?
2. How would the APY change if the interest were compounded semi-annually?
3. What is the difference in final amount if the initial deposit were $12,000?
4. How would continuous compounding affect the final amount?
5. How much interest will Kelsi earn in 1 year?

#### Tip:
Remember, APY accounts for the effect of compounding and represents the actual annual return on an investment.

A bank features a savings account that has an annual percentage rate of 3.6 % with interest compounded annually. Kelsi deposits $10,500 into the account. How much money will Kelsi have in the account in 1 year? Round answer to the nearest penny. What is the annual percentage yield (APY) for the savings account? Round to the nearest hundredth of a percent.

Learn how to calculate compound interest and annual percentage yield (APY) for a savings account with a $10,500 deposit at 3.6% annual percentage rate (APR), compounded annually. Step-by-step solution provided with key formulas explained. Suitable for students in Grades 9-12.

Math Problem Statement

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

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