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Let's analyze the problem in the image. Here is the translation and summary of the questions:

### Problem Summary:

1. **Peter** deposits 6,500 DKK in a bank with a fixed annual interest rate of 2.3%.
   - **(a)** How much money will be in the account after 5 years?

2. **Ditte** deposits 6,500 DKK in another bank. After 5 years, the amount has grown to 7,426 DKK.
   - **(b)** Determine the annual interest rate for this bank.

### Solution:

#### (a) Calculating Peter's Account Balance After 5 Years

The formula for compound interest is:
\[
A = P \times (1 + r)^n
\]
where:
- \( A \) is the amount after \( n \) years,
- \( P = 6,500 \) DKK (initial amount),
- \( r = 2.3\% = 0.023 \) (annual interest rate),
- \( n = 5 \) years.

Let's calculate \( A \).

#### (b) Finding Ditte's Annual Interest Rate

For Ditte, we know:
- Initial deposit \( P = 6,500 \) DKK,
- Final amount \( A = 7,426 \) DKK,
- Time period \( n = 5 \) years.

To find the annual interest rate \( r \), we use the compound interest formula and solve for \( r \):
\[
7426 = 6500 \times (1 + r)^5
\]

Now, I'll calculate the values for both parts.### Solution Results:

**(a)** The amount in Peter's account after 5 years will be **7,282.68 DKK**.

**(b)** The annual interest rate for Ditte's bank is approximately **2.70%**.

Would you like more details on the calculations, or do you have any questions?

### Related Questions:

1. How would the results change if the interest rates were compounded monthly instead of annually?
2. What would be the future value if Peter invested for 10 years instead of 5 years?
3. How long would it take for Ditte's investment to reach 8,000 DKK at the calculated interest rate?
4. What is the difference in total interest earned between Peter's and Ditte's investments after 5 years?
5. How would inflation affect the real value of Ditte's and Peter's investments over 5 years?

### Tip:
To compare different interest rates, always look at the compounded frequency (annually, semi-annually, monthly) since it can significantly impact the final amount.

Peter indsætter 6500 kr. i en bank til en fast årlig rente på 2,3 %. Ditte indsætter 6500 kr. på en konto i en anden bank. Efter 5 år er beløbet vokset til 7426 kr.

Learn how to calculate the compound interest for Peter's account with a 2.3% interest rate after 5 years and find the annual interest rate for Ditte's account that grows to 7426 DKK after 5 years. This math problem involves applying the compound interest formula.

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