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Lamar invested $5400 in an account that pays an annual interest rate of 2.3% , compounded daily. Assume there are 365 days in each year. Answer each part. If necessary, refer to the list of financial formulas

Let's solve each part of this financial problem step by step.

### (a) Find the amount in the account after one year, assuming no withdrawals are made.

This is a **compound interest** problem, where interest is compounded daily. The formula for compound interest is:

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

Where:
- $A$ = the amount of money accumulated after $t$ years, including interest.
- $P$ = the principal amount (initial investment) = $5400.
- $r$ = the annual interest rate (as a decimal) = 2.3% = 0.023.
- $n$ = the number of times the interest is compounded per year = 365 (since it's compounded daily).
- $t$ = the time the money is invested for in years = 1.

Let's compute $A$.

### (b) Find the effective annual interest rate (EAR), expressed as a percentage.

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

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

This formula takes into account the compounding periods. We already know:
- $r = 0.023$ (annual nominal interest rate).
- $n = 365$ (compounded daily).

Let me calculate both parts.Here are the results:

### (a) The amount in the account after one year:
\[
A = \$5525.64
\]

### (b) The effective annual interest rate (EAR):
\[
\text{EAR} = 2.33\%
\]

Would you like more details on any part of the solution?

Here are 5 related questions you might find helpful:
1. What happens if interest is compounded monthly instead of daily?
2. How would the calculation change for different principal amounts?
3. How does increasing the interest rate affect the effective annual rate?
4. What if the investment period is less than a year, say 6 months?
5. How does the frequency of compounding impact the final amount?

**Tip:** The more frequently interest is compounded, the higher the effective annual interest rate becomes.

Lamar invested $5400 in an account that pays an annual interest rate of 2.3%, compounded daily. Assume there are 365 days in each year. Find the amount in the account after one year and the effective annual interest rate.

Learn how to calculate the amount in an account after one year of compounded daily interest at a rate of 2.3%. This problem involves key financial math concepts such as compound interest and effective annual rate. Suitable for students in Grades 10-12.

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