https://r2.erweima.ai/mathbot/image/1726681712106g4ilvet8.jpg

Let's break down the problem step by step.

### Data from the table:
- **Years (Años)**: 2016, 2017, 2018, 2019, 2020
- **Investment (Inversión)** in thousands of euros (€): 16, 19, 20, 25, 20
- **Price Index (Índice de Precios)**: 110, 120, 118, 122, 119

### Tasks:
**a) Analyze the evolution of investment in real terms from 2016.**
- To express the investments in real terms (adjusted for inflation), we need to adjust them using the Price Index (Índice de Precios) with respect to 2016.
- The formula to convert nominal values to real values is:
  \[
  \text{Real Investment} = \frac{\text{Nominal Investment}}{\left( \frac{\text{Price Index of Year}}{\text{Price Index of Base Year}} \right)}
  \]
  where the base year is 2016 (Price Index = 110).

**b) Calculate the annual average real growth rate for the period 2016-2020.**
- After obtaining real investments, we can calculate the growth rate using the geometric mean:
  \[
  \text{Average Real Growth Rate} = \left( \frac{\text{Real Investment in 2020}}{\text{Real Investment in 2016}} \right)^{\frac{1}{4}} - 1
  \]
  This formula gives the average annual growth rate over the 4-year period.

**c) Estimate the nominal investment in 2021 assuming a 2% inflation rate and that real investment remains constant.**
- With inflation expected to be 2% and real investment unchanged, the nominal investment in 2021 can be found as:
  \[
  \text{Nominal Investment 2021} = \text{Real Investment 2020} \times (1 + \text{Inflation Rate})
  \]
Let's compute each part step-by-step. I'll first calculate the real investments for part (a).The real investments (in thousands of euros, adjusted for inflation with respect to 2016) for each year are as follows:

- **2016**: €16.00k
- **2017**: €17.42k
- **2018**: €18.64k
- **2019**: €22.54k
- **2020**: €18.49k

These values show how the investment evolved when adjusted for inflation.

Next, let's calculate the annual average real growth rate for the period 2016-2020 (part b). I'll compute this using the geometric mean formula.The average annual real growth rate of the investment from 2016 to 2020 is approximately **3.68%**.

Finally, let's estimate the nominal investment for 2021 assuming a 2% inflation rate and that the real investment remains constant (part c).The estimated nominal investment for 2021, assuming a 2% inflation rate and constant real investment, is approximately **€18.86k**.

Would you like more details on any part of the solution? Here are five follow-up questions that could help deepen your understanding:

1. How is the real growth rate affected by changes in the price index?
2. What is the difference between nominal and real investment in general?
3. How would the result change if the inflation rate for 2021 were different?
4. How does inflation impact long-term investments in financial markets?
5. Can we use the same method for predicting investments beyond 2021?

**Tip:** When calculating real values from nominal ones, always use the price index of a reference year for consistency across calculations.

A technological company invested in the stock market with €12,000 in 2014. Over the last five years, the company's investments and the Consumer Price Index (CPI) evolved as follows: 

Year: 2016, 2017, 2018, 2019, 2020 
Investment (in thousands of €): 16, 19, 20, 25, 20 
Price Index: 110, 120, 118, 122, 119. 

Tasks: 
(a) Analyze the evolution of the investment in real terms from 2016. 
(b) Calculate the annual average real growth rate for the period 2016-2020. 
(c) Estimate the nominal investment for 2021 assuming a 2% inflation rate and that real investment remains constant.

Explore the evolution of a company's investments in real terms from 2016 to 2020, accounting for inflation. Learn how to calculate real investments, the average real growth rate, and estimate future investments considering a 2% inflation rate.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation