A loan is being paid off by payments of 1,000, 2,000, ..., 10,000 at the end of years 1, 2, ..., 10. The effective annual interest rate is 18%. Determine the amount of interest in the 7th payment.

To determine the amount of interest in the 7th payment, we first need to calculate the outstanding loan balance at the end of year 6. The 7th payment consists of both interest on this balance and a principal repayment.

### Step 1: Understanding the Loan Payments
The loan payments are increasing linearly by 1,000 each year:
- 1st payment: 1,000
- 2nd payment: 2,000
- ...
- 10th payment: 10,000

Each payment is made at the end of the respective year.

### Step 2: Formula for Loan Balance
At the end of year \(n\), the loan balance consists of all the unpaid future payments, discounted to the end of year \(n\) using the given effective annual interest rate of 18%. 

The formula for discounting a future payment is:
\[
\text{Present Value} = \frac{\text{Future Payment}}{(1 + i)^n}
\]
where \(i = 0.18\) (the interest rate), and \(n\) is the number of years from the current year.

### Step 3: Calculating the Loan Balance After Year 6
The balance after year 6 is the present value of the remaining payments (years 7 to 10). Let's calculate the discounted value of each remaining payment:

- 7th payment (10,000): \( \frac{7,000}{(1 + 0.18)^1} \)
- 8: \( % \


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Learn how to calculate the interest portion of the 7th payment on a loan with increasing annual payments and an 18% effective interest rate. This detailed solution involves concepts like present value of payments and loan amortization. Suitable for high school or college-level finance students.

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