Corporate Finance (The Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
11th Edition
ISBN: 9780077861759
Author: Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan Professor
Publisher: McGraw-Hill Education
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Question
Chapter 4, Problem 74QP
Summary Introduction
To determine: The rate at which Rule of 72 is exact.
Rule of 72:
The rule of 72 is a thumb rule which states that if the interest rate is divided by 72 then the number of periods that the amount takes to double can be calculated. By this rule, the interest rate which is needed to double a money in a given time period can also be calculated.
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Students have asked these similar questions
The rule of 72’s states that the number of years for an investment to double is approximately 72 divided by the interest rate percentage. For example, about 12 years are required for an investment to double at 6% interest (12 years = 72/6). Find the exact rate required to double an investment in 6, 8, 9, 12, 18, and 24 years, and compare this with the approximate rule of 72’s rate.
Solutions manual only with formula used, without using Microsoft Excel.
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Example 1. Compound interest
When interest is compounded continuously, the rate of
change of the amount x of the investment is proportional
to the amount present. In this case, the proportionality
constant is the annual interest rate r (as a decimal); that
is, dx/dt = rx.
(a) If $2000 is invested at 8%, compounded
continuously, find an equation for the future value of the
investment as a function of time t, in years.
(b) How long will it take for the investment to double?
(c) What will be the future value of this investment after
35 years?
Chapter 4 Solutions
Corporate Finance (The Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
Ch. 4 - Prob. 1CQCh. 4 - Prob. 2CQCh. 4 - Prob. 3CQCh. 4 - Prob. 4CQCh. 4 - Time Value On subsidized Stafford loans, a common...Ch. 4 - Prob. 6CQCh. 4 - Prob. 7CQCh. 4 - Prob. 8CQCh. 4 - Prob. 9CQCh. 4 - Prob. 10CQ
Ch. 4 - Simple Interest versus Compound Interest First...Ch. 4 - Prob. 2QPCh. 4 - Prob. 3QPCh. 4 - Prob. 4QPCh. 4 - Prob. 5QPCh. 4 - Prob. 6QPCh. 4 - Calculating Present Values Imprudential, Inc., has...Ch. 4 - Calculating Rates of Return Although appealing to...Ch. 4 - Perpetuities An investor purchasing a British...Ch. 4 - Prob. 10QPCh. 4 - Prob. 11QPCh. 4 - Prob. 12QPCh. 4 - Calculating Annuity Present Value An investment...Ch. 4 - Calculating Perpetuity Values The Perpetual Life...Ch. 4 - Calculating EAR Find the EAR in each of the...Ch. 4 - Calculating APR Find the APR, in each of the...Ch. 4 - Calculating EAR First National Bank charges 10.3...Ch. 4 - Interest Rates Well-known financial writer Andrew...Ch. 4 - Calculating Number of Periods One of your...Ch. 4 - Prob. 20QPCh. 4 - Prob. 21QPCh. 4 - Simple Interest versus Compound Interest First...Ch. 4 - Calculating Annuities You are planning to save for...Ch. 4 - Prob. 24QPCh. 4 - Prob. 25QPCh. 4 - Prob. 26QPCh. 4 - Prob. 27QPCh. 4 - Annuity Present Values What is the present value...Ch. 4 - Annuity Present Values What is the value today of...Ch. 4 - Balloon Payments Audrey Sanborn has just arranged...Ch. 4 - Prob. 31QPCh. 4 - Prob. 32QPCh. 4 - Growing Annuity Southern California Publishing...Ch. 4 - Growing Annuity Your job pays you only once a year...Ch. 4 - Prob. 35QPCh. 4 - Prob. 36QPCh. 4 - Prob. 37QPCh. 4 - Calculating Loan Payments You need a 30-year,...Ch. 4 - Prob. 39QPCh. 4 - Calculating Present Values You just won the TVM...Ch. 4 - Prob. 41QPCh. 4 - Prob. 42QPCh. 4 - Prob. 43QPCh. 4 - Prob. 44QPCh. 4 - Prob. 45QPCh. 4 - Prob. 46QPCh. 4 - Prob. 47QPCh. 4 - Prob. 48QPCh. 4 - Prob. 49QPCh. 4 - Prob. 50QPCh. 4 - Calculating Annuities Due You want to lease a set...Ch. 4 - Prob. 52QPCh. 4 - Prob. 53QPCh. 4 - Prob. 54QPCh. 4 - Prob. 55QPCh. 4 - Prob. 56QPCh. 4 - Prob. 57QPCh. 4 - Prob. 58QPCh. 4 - Prob. 59QPCh. 4 - Prob. 60QPCh. 4 - Prob. 61QPCh. 4 - Prob. 62QPCh. 4 - Prob. 63QPCh. 4 - Prob. 64QPCh. 4 - Calculating the Number of Periods Your Christmas...Ch. 4 - Prob. 66QPCh. 4 - Prob. 67QPCh. 4 - Prob. 68QPCh. 4 - Prob. 69QPCh. 4 - Perpetual Cash Flows What is the value of an...Ch. 4 - Prob. 71QPCh. 4 - Prob. 72QPCh. 4 - Prob. 73QPCh. 4 - Prob. 74QPCh. 4 - Rule or 69.3 A corollary to the Rule of 72 is the...Ch. 4 - Prob. 1MCCh. 4 - Prob. 2MCCh. 4 - Prob. 3MCCh. 4 - Prob. 4MCCh. 4 - Prob. 5MCCh. 4 - Prob. 6MC
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- Which one is correct answer please confirm? Q4: Using the "Rule of 72," about how long will it take a sum of money to double in value if the annual interest rate is 9 percent? a. 8 years b. 7 years c. 9 years d. 10 yearsarrow_forward6. If the effective interest rate is i per period and you invest b dollars at time 0, then the value at time n is b(1 + i)”. For example, if at time 0 you invest $100 at an effective interest rate of 6% per year, then the value at time 1 is $100(1+0.06) = $106. dollars. At time 2, the value will be $100 (1 + 0.06)² = $112.36. Similarly, the present value (value at time 0) of $100 received 2 years from now would be $100(1+0.06)-²≈ $88.99. Sometimes it's convenient to define d = 1/(1 + i) so that we would have $100(1+i)n = $100d". If the interest rate per year is i compounded semiannually, then the effective annual interest rate is (¹ + 2)²³ - 1₁ 1. For example, if the interest rate is 6% per year compounded semiannually, the effective annual interest rate is 1 + .06 2 2 - 1 ≈ 6.09%. If the interest rate per year is i compounded quarterly, then the effective annual interest rate is 4 (¹ + 4) * - 1 1. (a) If the interest rate is 6% per year compounded quarterly, what is the effective…arrow_forwardIf the rate of inflation is 4.8%, what nominal interest rate is necessary for you to earn a 2.2% real interest rate on your investment? (Note: Be careful not to round any intermediate steps less than six decimal places.) The nominal interest rate is ____%. (Round to two decimal places.)arrow_forward
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