Question 1173640: Payments of $3,600, due 50 days ago, and $4,100, due in 40 days, are to be replaced by payments of $4,000 due today and the balance due in 30 days. What must the second payment be if the payee is to end up in an equivalent financial position? Money now earns 8.75%. Use 30 days from now as the focal date.
Second payment=
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to solve this problem step-by-step:
**1. Set up the Equation of Value at the Focal Date (30 Days from Now):**
* We need to bring all payments (both original and replacement) to the focal date and equate them.
* Let 'x' be the unknown second payment due in 30 days.
**2. Calculate the Value of the Original Payments at the Focal Date:**
* **Payment 1 ($3,600):**
* This payment was due 80 days before the focal date (50 days ago + 30 days to the focal date).
* Value at focal date: $3,600 * (1 + (0.0875/365)) ^ 80
* **Payment 2 ($4,100):**
* This payment was due 10 days before the focal date (40 days from now - 30 days to the focal date).
* Value at focal date: $4,100 * (1 + (0.0875/365)) ^ 10
**3. Calculate the Value of the Replacement Payments at the Focal Date:**
* **Payment 1 ($4,000):**
* This payment is made today, which is 30 days before the focal date.
* Value at focal date: $4,000 * (1 + (0.0875/365)) ^ 30
* **Payment 2 (x):**
* This payment is due at the focal date, so its value is simply 'x'.
**4. Create the Equation of Value:**
* Value of original payments = Value of replacement payments
* [$3,600 * (1 + (0.0875/365)) ^ 80] + [$4,100 * (1 + (0.0875/365)) ^ 10] = [$4,000 * (1 + (0.0875/365)) ^ 30] + x
**5. Solve for x:**
* Calculate the values:
* $3,600 * (1 + (0.0875/365)) ^ 80 ≈ $3,669.95
* $4,100 * (1 + (0.0875/365)) ^ 10 ≈ $4,109.83
* $4,000 * (1 + (0.0875/365)) ^ 30 ≈ $4,028.68
* Plug the values into the equation:
* $3,669.95 + $4,109.83 = $4,028.68 + x
* $7,779.78 = $4,028.68 + x
* Solve for x:
* x = $7,779.78 - $4,028.68
* x = $3,751.10
**Therefore, the second payment must be approximately $3,751.10.**
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