To find the combined equivalent value of the two payments today, we will need to calculate the present value of each payment. The formula for the present value (PV) is:

$PV = \frac{F}{(1 + r)^t}$

Where:

• $F$ is the future value (the payment amount),
• $r$ is the interest rate per period (annual rate divided by 12 if we're working in months),
• $t$ is the time in months until the payment is made.

Given:

• The interest rate is 7.30% per year or 0.073 annually.
• $r = \frac{0.073}{12} = 0.0060833$ per month.
• The payments are $6,300 each, one 4 months from now and the other 8 months from now.

Step 1: Calculate the present value of the first payment (4 months from now)

For the first payment, $F = 6,300$, $t = 4$ months, and $r = 0.0060833$.

$PV_1 = \frac{6,300}{(1 + 0.0060833)^4}$ $PV_1 = \frac{6,300}{(1.0060833)^4}$ $PV_1 = \frac{6,300}{1.024507}$ $PV_1 = 6,147.89$

Step 2: Calculate the present value of the second payment (8 months from now)

For the second payment, $F = 6,300$, $t = 8$ months, and $r = 0.0060833$.

$PV_2 = \frac{6,300}{(1 + 0.0060833)^8}$ $PV_2 = \frac{6,300}{(1.0060833)^8}$ $PV_2 = \frac{6,300}{1.050484}$ $PV_2 = 5,997.63$

Step 3: Combine the present values

Now, we will add the present values of both payments to get the combined present value.

$PV_{\text{combined}} = PV_1 + PV_2$ $PV_{\text{combined}} = 6,147.89 + 5,997.63$ $PV_{\text{combined}} = 12,145.52$

Thus, the combined equivalent value of the two payments today is $12,145.52.

Would you like further clarification on any step?

Here are some related questions:

1. How does changing the interest rate affect the present value of future payments?
2. What would the equivalent present value be if the interest rate were 5% instead of 7.30%?
3. How would the present value change if the payments were made 2 and 10 months from now instead of 4 and 8 months?
4. What happens to the combined present value if the interest rate is compounded quarterly instead of monthly?
5. How can we calculate the future value of these payments at the end of 12 months?

Tip: In financial calculations, the more frequent the compounding period (monthly vs annually), the greater the effect on the present value due to compounding interest.