Jonna takes out a loan of SEK 180,000 to be able to buy an apartment. The loan must be repaid with straight amortization once per quarter (every three months) over ten years. With each amortization, interest is also paid. Jonna's first payment is a total of SEK 7,470. What is the annual interest rate on the loan? Is it 7,5%, 0,67%, 6,6%, 0,55% or 9,6%

Let's calculate the annual interest rate again and compare it with the provided options.

### Step 1: Amortization Payment Calculation

- **Total loan amount**: SEK 180,000
- **Loan term**: 10 years
- **Payments per year**: 4 (quarterly payments)
- **Total number of payments**: \(10 \times 4 = 40\) payments

The straight amortization amount per quarter is:
\[
\text{Amortization per quarter} = \frac{180,000 \text{ SEK}}{40} = 4,500 \text{ SEK}
\]

### Step 2: Calculate the Interest for the First Payment

The first payment is SEK 7,470, which includes both amortization and interest. The interest portion is:
\[
\text{Interest for the first quarter} = 7,470 \text{ SEK} - 4,500 \text{ SEK} = 2,970 \text{ SEK}
\]

### Step 3: Determine the Quarterly Interest Rate

We use the interest formula:
\[
\text{Interest} = \text{Principal} \times \text{Quarterly Interest Rate}
\]
\[
2,970 \text{ SEK} = 180,000 \text{ SEK} \times r_{\text{quarterly}}
\]
\[
r_{\text{quarterly}} = \frac{2,970}{180,000} \approx 0.0165 \text{ (or 1.65%)}
\]

### Step 4: Calculate the Annual Interest Rate

The quarterly interest rate is approximately 1.65%. To convert this to an annual interest rate, we use the formula for compounding quarterly:
\[
r_{\text{annual}} = (1 + r_{\text{quarterly}})^4 - 1
\]
\[
r_{\text{annual}} = (1 + 0.0165)^4 - 1 \approx 0.0673 \text{ or } 6.73\%
\]

### Conclusion

The closest option to our calculated annual interest rate of **6.73%** is **6.6%**.

Therefore, the annual interest rate on the loan is **6.6%**.

Would you like any further clarification or details?

Here are some related questions:
1. How does the payment structure change over time in a straight amortization loan?
2. What is the difference between nominal and effective interest rates?
3. What would the total interest paid over the 10-year period be?
4. How would the interest calculation change if payments were made monthly instead of quarterly?
5. How does a change in the interest rate impact the overall cost of a loan?
6. What are the implications of paying extra toward the principal in a straight amortization loan?
7. How does the initial interest rate affect Jonna's total cost of the apartment?
8. What would be the impact of inflation on the loan repayments over time?

**Tip:** When dealing with loans and interest rates, always make sure to understand the difference between nominal rates (quoted) and effective rates (actual cost considering compounding).

Learn how to calculate the annual interest rate on a loan with quarterly payments. Understand the concepts of amortization, interest calculation, and quarterly compounding. Example calculation for a loan of SEK 180,000 with quarterly payments over 10 years.

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