Grandma Esther puts $2,500 in a CD (Certificate of Deposit) in which interest is compounded yearly at an annual interest rate of 5%. Grandma does not touch the account for 4 years. (a) How much does Grandma have in total in the account at the end of the 4 years? (b) How much interest did she earn in interest during the 4 years?

To solve the problem, we can use the formula for compound interest:

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

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

For this problem:
- $P = 2500$,
- $r = 0.05$,
- $n = 1$ (since the interest is compounded yearly),
- $t = 4$ years.

### (a) To calculate the total amount in the account at the end of 4 years:

\[
A = 2500\left(1 + \frac{0.05}{1}\right)^{1 \times 4} = 2500 \left(1.05\right)^4
\]

Now, calculate $(1.05)^4$:

\[
(1.05)^4 \approx 1.21550625
\]

So,

\[
A = 2500 \times 1.21550625 \approx 3038.77
\]

Thus, the total amount in the account at the end of 4 years is approximately **$3,038.77**.

### (b) To calculate the interest earned during the 4 years:

The interest earned is the difference between the total amount and the principal:

\[
\text{Interest earned} = A - P = 3038.77 - 2500 = 538.77
\]

Thus, Grandma earned **$538.77** in interest over the 4 years.

### Summary:
- (a) Grandma has **$3,038.77** in total at the end of 4 years.
- (b) She earned **$538.77** in interest.

Would you like further details or explanations?

### Related Questions:
1. How would the total amount change if the interest was compounded monthly instead of yearly?
2. What would happen if Grandma left the money in the account for 10 years instead of 4?
3. What is the formula for continuous compounding, and how would it affect this scenario?
4. How much interest would Grandma earn if the interest rate were 6% instead of 5%?
5. If Grandma added $500 to the account after 2 years, how would this affect the final balance?

### Tip:
In compound interest, the more frequently interest is compounded, the more interest is earned, as the interest itself earns interest more often.

Learn how to calculate the total amount and interest earned on a $2,500 CD compounded yearly at a 5% annual interest rate over 4 years. This problem explores the compound interest formula, exponents, and interest calculation, suitable for students in Grades 9-12.

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