A loan of $4,600 at 6.55% is to be repaid by three equal payments due two, four, and six months after the date on which the money was advanced.

Calculate the amount of each payment. Use the loan date as the focal date. (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Payment           $ 



To determine the amount of each equal payment, we use the concept of the **present value of annuities** and discount all payments to the loan date (focal date). The **formula for present value (PV) of a single future payment** is:

\[
PV = \frac{FV}{(1 + i)^n}
\]

where:  
- $ FV $ is the future payment amount,  
- $ i $ is the interest rate per period,  
- $ n $ is the number of periods.

### Given Data:
- Loan amount $ P = 4600 $
- Interest rate per year $ r = 6.55\% = 0.0655 $
- Payments are made at 2, 4, and 6 months.
- Monthly interest rate $ i = \frac{0.0655}{12} = 0.00545833 $

Let $ x $ be the amount of each equal payment. The present value equation is:

\[
4600 = \frac{x}{(1.00545833)^2} + \frac{x}{(1.00545833)^4} + \frac{x}{(1.00545833)^6}
\]

Now, solving for $ x $:  

1. Compute the discount factors:
   \[
   (1.00545833)^{-2} = 0.98916
   \]
   \[
   (1.00545833)^{-4} = 0.97844
   \]
   \[
   (1.00545833)^{-6} = 0.96789
   \]

2. Sum the discounted values:
   \[
   0.98916 + 0.97844 + 0.96789 = 2.93549
   \]

3. Solve for $ x $:
   \[
   x = \frac{4600}{2.93549} = 1567.06
   \]

### Final Answer:
\[
\mathbf{\$1567.06}
\]

Would you like a step-by-step breakdown or have any questions?  

Here are five related questions you might find useful:
1. How would the payments change if the interest rate increased to 8%?
2. What would be the total interest paid over the course of the loan?
3. How would the payments change if there were **four** equal payments instead of three?
4. How is the discount factor calculated, and why is it important?
5. What happens if payments are made **monthly** instead of every two months?

**Tip:** Always convert annual interest rates into the correct period before calculations to avoid errors.

A loan of $4,600 at 6.55% is to be repaid by three equal payments due two, four, and six months after the date on which the money was advanced. Calculate the amount of each payment. Use the loan date as the focal date. (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Learn how to calculate the equal repayment amount for a $4,600 loan at 6.55% interest, with payments due at 2, 4, and 6 months. This problem demonstrates key concepts like present value of annuities and discounting future payments. Suitable for students in Grades 11-12.

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