Which of the following correctly calculates the tuition index for 2025 based on the given values? A) 200 B) 125 C) 100 D) 150
Understand the Problem
The question asks which option correctly calculates the tuition index for the year 2025 based on provided values. It implies that there is a formula or method to determine the tuition index, and the user needs to identify the correct numerical answer from the options given.
Answer
$T \times (1 + r)^5$
Answer for screen readers
The correct tuition index for the year 2025 is $T \times (1 + r)^5$.
Steps to Solve
-
Identify Given Values
Determine the values you have for the tuition calculation. For example, if you have the base tuition and a growth rate, write them down. Let's say, base tuition is $T$ and growth rate is $r$. -
Understand the Formula
The tuition index can be calculated using a formula that often looks like this:
$$ T_{2025} = T \times (1 + r)^n $$
where $n$ is the number of years from the base year until 2025. -
Calculate the Number of Years
Determine how many years you will calculate for. For instance, if the base year is 2020, then $n = 2025 - 2020 = 5$. -
Plug Values into the Formula
Insert your values into the formula. For example:
$$ T_{2025} = T \times (1 + r)^5 $$ -
Calculate the Result
Perform the math calculations to find the tuition index for 2025. Ensure to calculate $(1 + r)$ raised to the power of 5, and then multiply by $T$.
The correct tuition index for the year 2025 is $T \times (1 + r)^5$.
More Information
This formula is commonly used for calculating inflation or growth over a number of years where you apply the growth rate to a base value repeatedly.
Tips
- Forgetting to convert percentages into decimals for calculations (e.g., $5%$ should be $0.05$).
- Not accounting for the correct number of years in the calculation.
- Miscalculating powers or forgetting to apply the formula correctly to all variables.
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