Yolanda invested $5,300
in an account that pays an annual interest rate of 3.3%
, compounded monthly. Answer each part. If necessary, refer to the list of financial formulas
.
(a)	Find the amount in the account after one year, assuming no withdrawals are made.
Do not round any intermediate computations, and round your answer to the nearest cent.
		
(b)	Find the effective annual interest rate, expressed as a percentage.
Do not round any intermediate computations, and round your answer to the nearest hundredth of a percent.
		


To solve this, we will use the compound interest formula:

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

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

### Given:
- $P = 5300$ (the principal amount).
- $r = 3.3\% = 0.033$.
- $n = 12$ (since the interest is compounded monthly).
- $t = 1$ year.

Let's solve each part:

---

### (a) Find the amount in the account after one year

Using the formula:

\[
A = 5300 \left(1 + \frac{0.033}{12}\right)^{12 \cdot 1}
\]

Now, I will calculate the result.

---

### (b) Find the effective annual interest rate

The effective annual interest rate (EAR) can be calculated using the following formula:

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

Substituting the given values:

\[
\text{EAR} = \left(1 + \frac{0.033}{12}\right)^{12} - 1
\]

I'll compute both parts now.### (a) The amount in the account after one year is approximately **$5,477.57**.

### (b) The effective annual interest rate (EAR) is approximately **3.35%**.

Would you like further details or have any questions? Here are some related questions to expand your understanding:

1. How does the number of compounding periods affect the final amount?
2. What would happen if the interest was compounded quarterly instead of monthly?
3. How would the result change if the interest rate was 5% instead of 3.3%?
4. What is the difference between simple interest and compound interest in this scenario?
5. How would the amount change if the investment duration was two years instead of one?

**Tip:** The more frequently interest is compounded, the more you earn due to the interest on interest effect.

Yolanda invested $5,300 in an account that pays an annual interest rate of 3.3%, compounded monthly. Answer each part: (a) Find the amount in the account after one year, assuming no withdrawals are made. (b) Find the effective annual interest rate, expressed as a percentage.

Discover how to calculate the final amount after one year for an investment of $5,300 at an annual interest rate of 3.3%, compounded monthly. Learn how to find the effective annual interest rate with detailed explanations and key formulas. Perfect for Grades 10-12 math students.

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