Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN: 9781337515610
Author: Crauder
Publisher: Cengage
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Chapter P, Problem 15E

The Rule of 72 This is a continuation of Exercise 14. Financial advisors sometimes use a rule of thumb known as Rule of 72 to get a rough estimate of the time it takes for an investment to double in value. For an investment that is compounded yearly at an interest rate of r % , this rule says it will take about 72 / r years for the investment to double. In this calculation, r is the integer interest rate rather than a decimal. Thus, if the interest rate is 8 % , we would use 72 / 8 rather than 72 / 0.08 .

For the remainder of this exercise, we will consider an investment that is compounded yearly at an interest rate of 13 % .

a. According to the Rule 72, how long will it take the investment to double in value?

Parts b and c of this exercise will check to see how accurate this estimate is for this particular case.

b. Using the answer you got from part a of this exercise, calculate the future value interest factor (as defined in Exercise 14). Is it exactly the same as your answer to the part a of Exercise 14?

c. If your initial investment was $ 5000 , use your answer from part b to calculate the future value. Did your investment exactly double?

Future Value Business and finance texts refer to the value of an investment at a future time as its future value. If an investment of P dollars is compounded yearly at an interest rate of r as a decimal, then the value of the investment after t years is given by

F u t u r e   V a l u e = P × 1 + r t .

In this formula, 1 + r t is known as the future value interest factor, so the formula above can be written as

F u t u r e   V a l u e = P × F u t u r e   v a l u e   i n t e r e s t   f a c t o r

Financial officers normally calculate this (or look it up in a table)

a. What future value interest factor will make an investment double?

b. Say you have an investment that is compounded yearly at a rate of 9 % .

Find the future value interest factor for a 7-year investment.

c. Use the results from part b to calculate the 7-year future value if your initial investment is $ 5000 .

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Chapter P Solutions

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

Ch. P - Pay Raise You receive a raise in your hourly pay...Ch. P - Heart Disease In a certain country, the number of...Ch. P - Trade Discount Often retailers sell merchandise at...Ch. P - Series Discount This is a continuation of Exercise...Ch. P - Present Value Present value is the amount of money...Ch. P - Future Value Business and finance texts refer to...Ch. P - The Rule of 72 This is a continuation of Exercise...Ch. P - The Truth in Lending Act Many lending agencies...Ch. P - The Size of the Earth The radius of the Earth is...Ch. P - When the Radius Increases a. A rope is wrapped...Ch. P - The Length of Earths Orbit The Earth is...Ch. P - Prob. 20ECh. P - Prob. 21ECh. P - Prob. 22ECh. P - Prob. 23ECh. P - Lean Body Weight in Males A persons lean body...Ch. P - Lean Body Weight in Females This is a continuation...Ch. P - Mannings Equation Hydrologists sometimes use...Ch. P - Relativistic Length A rocket ship travelling near...Ch. P - Equity in a Home When you purchase a home by...Ch. P - The Advantage Cash Card At the student union on a...Ch. P - Prob. 1SBECh. P - Prob. 2SBECh. P - Prob. 3SBECh. P - Basic Calculations 7.61.79.2Ch. P - Parenthesis and Grouping 7.3-6.82.5+1.8Ch. P - Prob. 6SBECh. P - Parentheses and Grouping 6+e+13Ch. P - Parentheses and Grouping -e+eCh. P - Prob. 9SBECh. P - Prob. 10SBECh. P - Prob. 11SBECh. P - Prob. 12SBECh. P - Prob. 13SBECh. P - Prob. 14SBECh. P - Prob. 15SBECh. P - Prob. 16SBECh. P - Arithmetic In Exercises S-16 through S-20, perform...Ch. P - Prob. 18SBECh. P - Prob. 19SBECh. P - Prob. 20SBECh. P - Prob. 21SBECh. P - Prob. 22SBECh. P - Prob. 23SBECh. P - Prob. 24SBECh. P - Prob. 25SBECh. P - Prob. 26SBECh. P - Prob. 27SBECh. P - Prob. 28SBECh. P - Prob. 29SBECh. P - Evaluating Formulas In Exercises S-21 through...Ch. P - Lending Money For a certain loan, the interest I...Ch. P - Monthly Payment For a certain instalment loan, the...Ch. P - Prob. 33SBECh. P - A Skydiver When a skydiver jumps from an airplane,...Ch. P - Future Value In certain savings scenarios, the...Ch. P - A Population of Deer The number N of deer in a...Ch. P - Prob. 37SBECh. P - Getting Three Sixes If we roll n fair dice, then...Ch. P - Prob. 1CRCh. P - Prob. 2CRCh. P - Prob. 3CRCh. P - Prob. 4CRCh. P - Keplers Third Law According to Keplers third law...Ch. P - Traffic Signal Traffic engineers study how long...
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