https://file.aiquickdraw.com/mathbot/file/1728653714058fzzwanjx.jpg

The problem in the image is written in Danish and appears to be a financial math problem involving compound interest. Here's a translation and breakdown of the key parts:

---

**Opgave 4**  
Oliver has agreed with his parents that if he leaves his confirmation money (25,000 kr) in the bank (without using any of it), his parents will give him an interest of 6% per year.  

- **a)** How much will Oliver have after the first year?  
- **b)** How much will Oliver have in total after 3 years?

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### Solution:

#### a) After the first year:
We are calculating the amount after one year using simple interest formula:
\[
A = P \times (1 + r)
\]
Where:
- \(A\) = amount after 1 year
- \(P = 25,000\) kr (the initial amount)
- \(r = 6\% = 0.06\) (interest rate)

\[
A = 25,000 \times (1 + 0.06) = 25,000 \times 1.06 = 26,500 \text{ kr}
\]

So, after the first year, Oliver will have **26,500 kr**.

#### b) After 3 years:
We now calculate the compound interest over 3 years:
\[
A = P \times (1 + r)^t
\]
Where:
- \(A\) = amount after 3 years
- \(P = 25,000\) kr
- \(r = 6\%\)
- \(t = 3\) years

\[
A = 25,000 \times (1 + 0.06)^3 = 25,000 \times 1.06^3 = 25,000 \times 1.191016 = 29,775.4 \text{ kr}
\]

After 3 years, Oliver will have **29,775.40 kr**.

---

Would you like more details, or do you have any further questions?

Here are 5 related questions:
1. What would the amount be if the interest rate was 8% instead of 6% after 3 years?
2. How much interest would Oliver earn in total over 3 years?
3. What would happen if Oliver withdraws some money at the end of the second year?
4. How would the total amount change if the interest was compounded monthly instead of yearly?
5. How much more would Oliver have after 5 years compared to 3 years?

**Tip:** When dealing with compound interest, always remember that the interest is applied on the accumulated total, not just the initial amount!

Oliver har aftalt med mor og far, at hvis han lader sine konfirmationspenge (kr. 25.000) stå i banken (og ikke bruger af dem), så vil hans forældre give ham 6% pr. år i rente. a) Hvad har Oliver i alt efter det første år? b) Hvad har han stående efter 3 år?

Learn how to calculate compound interest on Oliver's confirmation money of 25,000 kr left in the bank at 6% interest for one and three years. This detailed solution covers both first-year and third-year totals, using key algebraic formulas suitable for high school students.

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