Question

A loan payment of $1200.00 was due 10 days ago and another payment of $900.00 is due 60 days from now. What single payment 120 days from now will pay off the two obligations if interest is to be 2% and the agreed focal date is 120 days from now? The value of the payment is $ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Answer 1

To calculate the single payment that will pay off the two loan obligations, you need to find the present value of each payment and add them together using the present value formula.

Step-by-step explanation:

To calculate the single payment that will pay off the two loan obligations, we need to find the present value of each payment and add them together. Let's break it down step-by-step:

1. The first payment of $1200.00 was due 10 days ago, so it is already in the past. We need to find its present value.
2. The second payment of $900.00 is due 60 days from now. We also need to find its present value.
3. Finally, we need to find the single payment 120 days from now that will pay off both obligations.

Using the present value formula, which is PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods, we can calculate the present value of each payment and then add them together to find the single payment.

Let's calculate:

1. Present value of the first payment:

PV1 = 1200 / (1 + 0.02)^(10/365)

2. Present value of the second payment:

PV2 = 900 / (1 + 0.02)^(60/365)

3. Calculate the single payment 120 days from now:

PV = PV1 + PV2

Now, plug in the values and calculate to find the single payment:

PV = (1200 / (1 + 0.02)^(10/365)) + (900 / (1 + 0.02)^(60/365))

Round the final answer to the nearest cent as needed.