/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 73 College Tuition If college tuiti... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

College Tuition If college tuition is currently \(\$ 8000\) per year, inflating at \(6 \%\) per year, what will be the cost of tuition in 10 years?

Short Answer

Expert verified
The cost of tuition in 10 years will be approximately $14,327.

Step by step solution

01

Understand the Problem

We need to find the future cost of college tuition in 10 years, given an annual inflation rate. The initial cost is \( \$ 8000 \) and the inflation rate is \( 6\% \).
02

Identify the Relevant Formula

The future value of a financial quantity experiencing constant growth can be calculated using the formula for compound interest: \[ FV = PV \times (1 + r)^n \]where \( FV \) is the future value, \( PV \) is the present value, \( r \) is the growth rate, and \( n \) is the number of periods.
03

Substitute Values into the Formula

We substitute the known values into the formula: - \( PV = 8000 \)- \( r = 0.06 \) (since 6% = 0.06)- \( n = 10 \)This gives:\[ FV = 8000 \times (1 + 0.06)^{10} \]
04

Calculate the Future Value

First, calculate the expression inside the parentheses:\[ 1 + 0.06 = 1.06 \]Next, raise this to the power of 10:\[ 1.06^{10} \approx 1.790847 \]Finally, multiply this result by 8000:\[ FV = 8000 \times 1.790847 \approx 14326.776 \]
05

Round the Answer

Round the calculated future value to the nearest dollar:\[ FV \approx 14327 \]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

College Tuition
College tuition is the amount of money students pay to attend an academic institution, usually on an annual basis. Over the years, tuition fees have been a growing concern for students and their families, especially given the continuous increase in education costs.
Several factors contribute to changes in college tuition, including:
  • Operational costs for colleges, like faculty salaries and facility maintenance.
  • Government funding levels, which can subsidize or alleviate costs.
  • Inflation, which affects nearly all sectors of the economy.
It's important to be aware of these factors as they not only influence the present but also future tuition costs that affect budgeting and financial planning for education.
Inflation Rate
The inflation rate is essentially the percentage increase in the general price level of goods and services in an economy over a period, typically an annual rate. This measure is crucial because it reflects how purchasing power diminishes over time when prices rise.
When it comes to college tuition, inflation can have a notable impact as it increases the cost of education year by year. In the exercise at hand, an inflation rate of 6% implies that tuition costs are expected to grow by this percentage annually.
Understanding how inflation works is essential for:
  • Projecting increases in costs for long-term planning.
  • Comparing current and future economic costs effectively.
  • Making informed financial decisions.
In our example, a consistent 6% rise means that every year, the tuition becomes more expensive, steadily increasing over a ten-year span.
Future Value Calculation
Future value calculation is a fundamental concept in finance, allowing individuals to determine how much a certain amount of money today will grow over time with a given interest or growth rate. This method is commonly used for calculating savings, investments, or expected expenses like college tuition.
The formula for future value with compound interest is:\[ FV = PV \times (1 + r)^n \]where:
  • \(FV\) stands for future value.
  • \(PV\) is the present value or the current amount.
  • \(r\) is the rate of interest or growth, expressed as a decimal.
  • \(n\) is the number of years.
This formula helps account for inflation by showing what the equivalent value will be in the future.
For example, with an inflation rate of 6%, the calculation \(8000 \times (1 + 0.06)^{10}\) gives us a future value of approximately 14,327 dollars for college tuition, indicating how much one would need to save or plan for a decade from now.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The table lists the atmospheric density \(y\) in kilograms per cubic meter \(\left(\mathrm{kg} / \mathrm{m}^{3}\right)\) at an altitude of \(x\) meters. $$\begin{array}{ccccc} x(m) & 0 & 5000 & 10,000 & 15,000 \\ y\left(k g / m^{3}\right) & 1.2250 & 0.7364 & 0.4140 & 0.1948 \end{array}$$ $$\begin{array}{rllll} \boldsymbol{x}(\mathrm{m}) & 20,000 & 25,000 & 30,000 \\\ y\left(\mathrm{kg} / \mathrm{m}^{3}\right) & 0.0889 & 0.0401 & 0.0184 \end{array}$$ (a) Find a function \(f\) that models the data. (b) Prodict the density at 7000 meters. (The actual value is \(.0.59 \mathrm{kg} / \mathrm{m}^{3} .\))

Heavier birds tend to have larger wings than smaller birds. For one species of bird, the table lists the area \(A\) of the bird's wing in square inches if the bird weighs \(w\) pounds. $$\begin{array}{rccccc}w(\mathrm{b}) & 2 & 6 & 10 & 14 & 18 \\\\\hline A(w)\left(\mathrm{in}^{2}\right) & 160 & 330 & 465 & 580 & 685\end{array}$$ (a) Find a function that models the data. (b) Graph \(A\) and the data. (c) What weight corresponds to a wing area of 500 square inches?

Solve each equation. Approximate answers to four decimal places when appropriate. $$2 \log 5 x=4$$

Runvay Length There is a relation between an airplane's weight \(x\) and the runway length \(L\) required for takeoff. For some airplanes the minimum runway length \(L\) in thousands of feet may be modeled by \(L(x)=3 \log x,\) where \(x\) is measured in thousands of pounds. (Sourcet. I. Haefner, Introduction to Thangortation Systems.) (a) Graph \(L\) for \(0

Trains The faster a locomotive travels, the more horsepower is needed. The formula \(H(x)=0.157(1.033)^{x}\) calculates this horsepower for a level track. The input \(x\) is in miles per hour and the output \(H(x)\) is the horsepower required per ton of cargo. (a) Evaluate \(H(30)\) and interpret the result. (b) Determine the horsepower needed to move a 5000 ton train 30 miles per hour. (c) Some types of locomotives are rated for 1350 horsepower. How many locomotives of this type would be needed in part (b)?

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.