https://r2.erweima.ai/mathbot/image/1726523922682nqjvwbpz.jpg

This problem involves calculating the present value of two debts with different due dates, each worth $150,000, at a simple annual interest rate of 35%. Then, after 30 days, the debtor decides to pay off the debt early. Let's break the problem into steps:

### Step 1: Determine the present value of the total debt.

- We have two documents:
  - First document due in 60 days.
  - Second document due in 90 days.

The goal is to calculate the equivalent present value (valor de contado) using the interest rate given.

We will use the formula for present value with simple interest:

\[
PV = \frac{F}{1 + (i \cdot t)}
\]

Where:
- $ PV $ is the present value.
- $ F $ is the face value (future amount) of the document.
- $ i $ is the interest rate (in this case, annual simple interest).
- $ t $ is the time in years (since the rate is annual).

### Step 2: Convert the time periods to years.

- 60 days = $ \frac{60}{365} $ years.
- 90 days = $ \frac{90}{365} $ years.

The interest rate $ i = 35\% $ or $ 0.35 $.

### Step 3: Calculate the present value for each document.

For the first document (due in 60 days):

\[
PV_1 = \frac{150,000}{1 + (0.35 \cdot \frac{60}{365})}
\]

For the second document (due in 90 days):

\[
PV_2 = \frac{150,000}{1 + (0.35 \cdot \frac{90}{365})}
\]

### Step 4: Add the present values to get the total present value of the debt.

\[
PV_{total} = PV_1 + PV_2
\]

### Step 5: Determine how much the debtor needs to pay after 30 days.

If the debtor wants to settle the debt after 30 days, we need to adjust the time remaining for each document:
- First document: 60 - 30 = 30 days remaining.
- Second document: 90 - 30 = 60 days remaining.

We'll use the simple interest formula again to determine how much the debtor needs to pay at that point for both debts:

\[
Debt_1 = 150,000 \cdot (1 + 0.35 \cdot \frac{30}{365})
\]
\[
Debt_2 = 150,000 \cdot (1 + 0.35 \cdot \frac{60}{365})
\]

Now, I'll calculate these values.1. The total present value (valor de contado) of the debt is approximately **$279,922.61**.

2. If the debtor decides to pay off the debt after 30 days, the total amount they need to pay is **$312,945.21**.

Would you like more details on any part of the solution or further explanations?

Here are 5 related questions you might find useful:
1. How is simple interest different from compound interest in debt calculations?
2. How does the repayment period affect the present value of future payments?
3. What would happen to the present value if the interest rate were compounded monthly?
4. How does the payment amount change if the interest rate were higher or lower?
5. Can we apply the same method to calculate debts for periods longer than a year?

**Tip:** When calculating interest, always ensure the time unit (days, months, years) matches the interest rate's time frame to avoid errors in calculation.

Si se posee 2 documentos cuyos vencimientos son a 60 y 90 de plazo respectivamente por un valor de $150.000 cada uno por la venta de un bien, se desea determinar cual es el valor de contado del bien vendido si la tasa aplicada en la operación es del 35% anual simple. Si transcurridos 30 días el comprador recibió un dinero extra y decide cancelar su deuda ¿Cuánto tendrá que abonar?

Resuelve un problema financiero de cómo determinar el valor de contado de un bien vendido con dos documentos con vencimientos a 60 y 90 días, a una tasa de interés simple anual del 35%. Además, calcula el monto a pagar si el comprador desea cancelar su deuda anticipadamente después de 30 días.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation