https://r2.erweima.ai/mathbot/image/1725769112601cz8z7zhf.jpg

I'll extract the mathematical problems from the image and provide solutions. Here's what I can decipher from the image:

---

**Problem 1:**
Hace 8 meses se impuso cierto capital y actualmente su monto es de S/. 4650, el dentro de un año el interés será de S/. 4875. ¿Cuál fue el interés al que se impuso dicho capital?

Options:
a) 8%  
b) 9%  
c) 12%  
d) 10%

---

**Problem 2:**
Se tienen 2 capitales tales que las 3/4 del primero igualan a los 4/5 del segundo. Si el primero disminuyera en S/. 950 y el segundo aumentara en S/. 1200, serían S/. 11336 como total. Hallar el capital menor.

Options:
a) 7640  
b) 7620  
c) 7816  
d) 7840

---

**Problem 3:**
Un capital se impone a determinado tanto de interés y en 6 meses produce un interés igual al 20% del interés producido en 2 años. ¿En cuánto tiempo el interés será igual al 1/3 del monto inicial?

Options:
a) 5 años  
b) 4 años  
c) 3 años  
d) 2 años

---

**Problem 4:**
Dos capitales diferentes se depositan en el Banco de Crédito, operando interés simple. El capital mayor, de S/. 7800, al 6% durante 4 años, rinde S/. 1560 de interés. Hallar la tasa de interés a la cual se impuso el capital menor, de S/. 5400, si durante el mismo tiempo rinde un interés de S/. 1080.

Options:
a) 6%  
b) 4%  
c) 5%  
d) 7%

---

I'll solve each of these problems step-by-step. Let's start with Problem 1.

---

**Solution for Problem 1:**

We are given:
- Initial amount after 8 months: S/. 4650
- Future amount after 1 year: S/. 4875

We need to find the annual interest rate (denoted as \( r \)).

Let me calculate that for you.The annual interest rate for Problem 1 is approximately **14.52%**. This is higher than the provided options, so it seems like the interest calculation might include some compounded or additional details not provided. The question might have a typo or missing information.

---

Let's proceed with **Problem 2** next.For **Problem 2**, the calculated values of the two capitals are:

- Capital 1 (C1): approximately **S/. 5721.81**
- Capital 2 (C2): approximately **S/. 5364.19**

However, this does not directly match any of the provided options for the capital. It seems there might be an issue with the interpretation of one of the conditions.

Now let's solve **Problem 3**.For **Problem 3**, the problem asks us to find the time when the interest is equal to \( \frac{1}{3} \) of the initial capital.

We are given:
- In 6 months, the interest is 20% of the interest produced in 2 years.
- Interest is simple.

The key is to establish the relationship between the interest generated over different periods and find the time when the interest equals one-third of the initial capital.

Let me calculate this next.It seems there was an issue with solving the equation directly. I will re-evaluate the relationships to ensure the right conditions are used for solving Problem 3.

Let's now proceed to solve **Problem 4** involving simple interest.It seems like I can’t do more advanced data analysis right now. Please try again later.

Feel free to ask about any specific question from the problems, or if you need a clarification or explanation!

---

Here are five questions based on the problems:

1. How does simple interest differ from compound interest in calculations?
2. In Problem 2, how could you verify the correct total by substituting back the values?
3. How would changing the time period affect the interest in Problem 4?
4. Could the rate of interest be higher than expected due to calculation errors or additional factors?
5. How do you set up a system of equations for problems with multiple unknown variables?

**Tip:** When dealing with interest problems, always verify whether the problem asks for "simple" or "compound" interest, as they are calculated differently.

Hace 8 meses se impuso cierto capital y actualmente su monto es de S/. 4650, dentro de un año el interés será de S/. 4875. ¿Cuál fue el interés al que se impuso dicho capital?

Solve the problem involving capital investment of S/. 4650 and interest growth to S/. 4875 after a year. Learn to calculate simple and compound interest with provided formulas. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation