Explanation A perpetuity is an annuity in which the payments go on forever. Use the formula for the present value of an ordinary annuity: P = R [ 1 − ( 1 + i ) − n i ] Here, P is the present value, R is the periodic payment, i is the interest rate per period, and n is the number of periods. Observe the changes in the value of P when n gets larger and larger for a given value of R and i . For example, take R = $ 50 , 000 , i = 5 % = 0.05 , and n = 5 to obtainthe value of P as follows: P ( n = 5 ) = 50 , 000 [ 1 − ( 1 + 0.05 ) − 5 0.05 ] = 1 , 000 , 000 [ 1 − 0.7835261 ] = 1 , 000 , 000 × 0.2164738 = 216 , 473.83 Increase the value of n to 10: P ( n = 10 ) = 50 , 000 [ 1 − ( 1 + 0.05 ) − 10 0.05 ] = 1 , 000 , 000 [ 1 − 0.613913 ⋯ ] = 1 , 000 , 000 × 0.386086 ⋯ = 386 , 086.75 For n = 20 , the present value will be as follows: P ( n = 20 ) = 50 , 000 [ 1 − ( 1 + 0.05 ) − 20 0.05 ] = 1 , 000 , 000 [ 1 − 0.376889 ] = 1 , 000 , 000 × 0

11th Edition

ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

See similar textbooks

Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…

Videos

Question

Chapter 5.3, Problem 56E

To determine

Why the present value of perpetuity is given by P=Ri?

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 5.3, Problem 55E

Chapter 5.3, Problem 57E

Students have asked these similar questions

Not use ai please

Solve the equation. Write the smaller answer first. 2 (x-6)² = 36 x = Α x = Previous Page Next Page

Chapter 5 Solutions

Finite Mathematics (11th Edition)

Ch. 5.1 - 1. What factors determine the amount of interest...Ch. 5.1 - In your own words, describe the maturity value of...Ch. 5.1 - 3. What is meant by the present value of...Ch. 5.1 - We calculated the loan in Example 2(b) assuming...Ch. 5.1 - Find the simple interest. $25,000 at 3% for 9...Ch. 5.1 - Find the simple interest. 6. $4289 at 4.5% for...Ch. 5.1 - Find the simple interest. 7. $1974 at 6.3% for...Ch. 5.1 - Find the simple interest. 8. $6125 at 1.25% for...Ch. 5.1 - Find the simple interest. Assume a 360-day year....Ch. 5.1 - Find the simple interest. Assume a 360-day...

Ch. 5.1 - Find the maturity value and the amount of simple...Ch. 5.1 - Find the maturity value and the amount of simple...Ch. 5.1 - Find the maturity value and the amount of simple...Ch. 5.1 - Find the maturity value and the amount of...Ch. 5.1 - 15. Explain the difference between simple...Ch. 5.1 - Prob. 16E Ch. 5.1 - 17. What is the difference between t and n? Ch. 5.1 - In Figure 2, one line is straight and the other is...Ch. 5.1 - Find the compound amount for each deposit and the...Ch. 5.1 - Find the compound amount for each deposit and...Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Find the compound amount for each deposit and the...Ch. 5.1 - Find the interest rate for each deposit and...Ch. 5.1 - Prob. 26E Ch. 5.1 - Find the interest rate for each deposit and...Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Find the effective rate corresponding to each...Ch. 5.1 - Find the effective rate corresponding to each...Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Find the present value (the amount that should be...Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Find the present value (the amount that should...Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Find the doubling time for each of the...Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - Prob. 49E Ch. 5.1 - 50. Delinquent Taxes An accountant for a...Ch. 5.1 - Savings A $1500 certificate of deposit held for 75...Ch. 5.1 - Prob. 52E Ch. 5.1 - Cash Advance Fees According to an advertisement,...Ch. 5.1 - Prob. 54E Ch. 5.1 - Investments Suppose $10,000 is invested at an...Ch. 5.1 - 56. Investments In Exercise 55, notice that as...Ch. 5.1 - Prob. 57E Ch. 5.1 - Prob. 58E Ch. 5.1 - Student Loan Upon graduation from college, Warren...Ch. 5.1 - Comparing Investments Two partners agree to invest...Ch. 5.1 - Prob. 61E Ch. 5.1 - Prob. 62E Ch. 5.1 - Negative Interest Under certain conditions, Swiss...Ch. 5.1 - Negative Interest Under certain conditions,...Ch. 5.1 - Savings On January 1, 2010, Jack deposited $1000...Ch. 5.1 - Prob. 66E Ch. 5.1 - Prob. 67E Ch. 5.1 - Prob. 68E Ch. 5.1 - Prob. 69E Ch. 5.1 - 70. Effective Rate Determine the effective...Ch. 5.1 - Prob. 71E Ch. 5.1 - Prob. 72E Ch. 5.1 - Buying a House Cara Tilley wants to have $30,000...Ch. 5.1 - Prob. 74E Ch. 5.1 - Doubling Time Use the ideas from Example 11 to...Ch. 5.1 - Prob. 76E Ch. 5.1 - Prob. 77E Ch. 5.1 - Prob. 78E Ch. 5.1 - Prob. 79E Ch. 5.1 - Prob. 80E Ch. 5.2 - Find the fifth term of each geometric sequence. a...Ch. 5.2 - Prob. 2E Ch. 5.2 - Prob. 3E Ch. 5.2 - Prob. 4E Ch. 5.2 - Find the fifth term of each geometric sequence. a...Ch. 5.2 - Find the fifth term of each geometric...Ch. 5.2 - Find the fifth term of each geometric...Ch. 5.2 - Prob. 8E Ch. 5.2 - Prob. 9E Ch. 5.2 - Find the sum of the first four terms for each...Ch. 5.2 - Prob. 11E Ch. 5.2 - Prob. 12E Ch. 5.2 - Prob. 13E Ch. 5.2 - Prob. 14E Ch. 5.2 - Find the sum of the first four terms for each...Ch. 5.2 - Prob. 16E Ch. 5.2 - Prob. 17E Ch. 5.2 - Prob. 18E Ch. 5.2 - Prob. 19E Ch. 5.2 - Find the future value of each ordinary annuity....Ch. 5.2 - Prob. 21E Ch. 5.2 - Find the future value of each ordinary annuity,...Ch. 5.2 - Find the future value of each ordinary annuity,...Ch. 5.2 - Prob. 24E Ch. 5.2 - Find the future value of each ordinary annuity, if...Ch. 5.2 - Prob. 26E Ch. 5.2 - Find the future value of each ordinary annuity,...Ch. 5.2 - Prob. 28E Ch. 5.2 - Determine the interest rate needed to accumulate...Ch. 5.2 - Determine the interest rate needed to accumulate...Ch. 5.2 - Find the periodic payment that will amount to...Ch. 5.2 - Prob. 32E Ch. 5.2 - Prob. 33E Ch. 5.2 - Find the amount of each payment to be made into...Ch. 5.2 - Find the amount of each payment to be made into a...Ch. 5.2 - Prob. 36E Ch. 5.2 - Prob. 37E Ch. 5.2 - Prob. 38E Ch. 5.2 - Find the future value of each annuity due....Ch. 5.2 - Find the future value of each annuity due. Assume...Ch. 5.2 - Prob. 41E Ch. 5.2 - Prob. 42E Ch. 5.2 - Prob. 43E Ch. 5.2 - Prob. 44E Ch. 5.2 - Find the future value of each annuity due. Then...Ch. 5.2 - Prob. 46E Ch. 5.2 - Prob. 47E Ch. 5.2 - Prob. 48E Ch. 5.2 - Prob. 49E Ch. 5.2 - 50. Retirement Planning A 45-year-old man puts...Ch. 5.2 - 51. Retirement Planning At the end of each...Ch. 5.2 - Prob. 52E Ch. 5.2 - Prob. 53E Ch. 5.2 - Prob. 54E Ch. 5.2 - Individual Retirement Accounts Suppose a...Ch. 5.2 - Prob. 56E Ch. 5.2 - Prob. 57E Ch. 5.2 - Prob. 58E Ch. 5.2 - Prob. 59E Ch. 5.2 - Savings A father opened a savings account for his...Ch. 5.2 - Prob. 61E Ch. 5.2 - Savings Nic Daubenmire deposits $10,000 at the...Ch. 5.2 - Prob. 63E Ch. 5.2 - Prob. 64E Ch. 5.2 - Lottery In a 1992 Virginia lottery, the jackpot...Ch. 5.2 - Prob. 66E Ch. 5.2 - Prob. 67E Ch. 5.2 - Prob. 68E Ch. 5.3 - Explain the difference between the present value...Ch. 5.3 - 2. What does it mean to amortize a loan? Ch. 5.3 - Prob. 3E Ch. 5.3 - Find the present value of each ordinary annuity....Ch. 5.3 - Find the present value of each ordinary...Ch. 5.3 - Find the present value of each ordinary...Ch. 5.3 - Find the present value of each ordinary annuity....Ch. 5.3 - Find the present value of each ordinary...Ch. 5.3 - Find the lump sum deposited today that will yield...Ch. 5.3 - Find the lump sum deposited today that will yield...Ch. 5.3 - Find (a) the payment necessary to amortize each...Ch. 5.3 - Find (a) the payment necessary to amortize each...Ch. 5.3 - Find (a) the payment necessary to amortize each...Ch. 5.3 - Find (a) the payment necessary to amortize each...Ch. 5.3 - Find (a) the payment necessary to amortize each...Ch. 5.3 - Find (a) the payment necessary to amortize each...Ch. 5.3 - Suppose that in the loans described in Exercises...Ch. 5.3 - Suppose that in the loans described in Exercises...Ch. 5.3 - Suppose that in the loans described in Exercises...Ch. 5.3 - Suppose that in the loans described in Exercises...Ch. 5.3 - Prob. 21E Ch. 5.3 - Prob. 22E Ch. 5.3 - Prob. 23E Ch. 5.3 - Prob. 24E Ch. 5.3 - What sum deposited today at 5% compounded annually...Ch. 5.3 - What lump sum deposited today at 8% compounded...Ch. 5.3 - Prob. 27E Ch. 5.3 - Prob. 28E Ch. 5.3 - Prob. 29E Ch. 5.3 - Find the monthly house payments necessary to...Ch. 5.3 - Prob. 31E Ch. 5.3 - Suppose that in the loans described in Exercise...Ch. 5.3 - Suppose that in the loans described in Exercise...Ch. 5.3 - Prob. 34E Ch. 5.3 - House Payments Calculate the monthly payment and...Ch. 5.3 - Prob. 36E Ch. 5.3 - Prob. 37E Ch. 5.3 - Prob. 38E Ch. 5.3 - Prob. 39E Ch. 5.3 - 40. New Car Financing In 2014, some dealers...Ch. 5.3 - Prob. 41E Ch. 5.3 - Prob. 42E Ch. 5.3 - Prob. 43E Ch. 5.3 - Prob. 44E Ch. 5.3 - Installment Buying In Exercises 44-46, prepare an...Ch. 5.3 - Prob. 46E Ch. 5.3 - Prob. 47E Ch. 5.3 - Prob. 48E Ch. 5.3 - House Payments Jason Hoffa buys a house for...Ch. 5.3 - 50. House Payments The Chavara family buys a...Ch. 5.3 - Prob. 51E Ch. 5.3 - Prob. 52E Ch. 5.3 - Prob. 53E Ch. 5.3 - Prob. 54E Ch. 5.3 - Prob. 55E Ch. 5.3 - Prob. 56E Ch. 5.3 - Prob. 57E Ch. 5 - Lorri Morgan received $50 on her 16th birthday,...Ch. 5 - At the beginning of the year, Yvette Virgil...Ch. 5 - Prob. 3EA Ch. 5 - Prob. 4EA Ch. 5 - People often lose money on investments. Karen...Ch. 5 - Prob. 1RE Ch. 5 - Prob. 2RE Ch. 5 - Prob. 3RE Ch. 5 - Prob. 4RE Ch. 5 - Prob. 5RE Ch. 5 - Prob. 6RE Ch. 5 - Prob. 7RE Ch. 5 - Prob. 8RE Ch. 5 - Prob. 9RE Ch. 5 - Prob. 10RE Ch. 5 - Prob. 11RE Ch. 5 - Find the simple interest for each loan. $4902 at...Ch. 5 - Prob. 13RE Ch. 5 - Prob. 14RE Ch. 5 - Prob. 15RE Ch. 5 - Prob. 16RE Ch. 5 - Prob. 17RE Ch. 5 - Find the compound amount in each loan. 18....Ch. 5 - Prob. 19RE Ch. 5 - Prob. 20RE Ch. 5 - Prob. 21RE Ch. 5 - Find the amount of interest earned by each...Ch. 5 - Find the amount of interest earned by each...Ch. 5 - Prob. 24RE Ch. 5 - Prob. 25RE Ch. 5 - Find the present value of each amount. $17,650 in...Ch. 5 - Prob. 27RE Ch. 5 - Prob. 28RE Ch. 5 - Prob. 29RE Ch. 5 - Prob. 30RE Ch. 5 - Prob. 31RE Ch. 5 - Prob. 32RE Ch. 5 - Prob. 33RE Ch. 5 - Prob. 34RE Ch. 5 - Prob. 35RE Ch. 5 - Prob. 36RE Ch. 5 - Prob. 37RE Ch. 5 - Prob. 38RE Ch. 5 - Find the future value of each annuity and the...Ch. 5 - Find the future value of each annuity and the...Ch. 5 - Prob. 41RE Ch. 5 - Prob. 42RE Ch. 5 - Prob. 43RE Ch. 5 - Prob. 44RE Ch. 5 - Prob. 45RE Ch. 5 - Find the amount of each payment that must be...Ch. 5 - Prob. 47RE Ch. 5 - Prob. 48RE Ch. 5 - Prob. 49RE Ch. 5 - Find the present value of each ordinary...Ch. 5 - Prob. 51RE Ch. 5 - Prob. 52RE Ch. 5 - Find the present value of each ordinary annuity....Ch. 5 - Prob. 54RE Ch. 5 - Find the amount of the payment necessary to...Ch. 5 - Prob. 56RE Ch. 5 - Prob. 57RE Ch. 5 - Prob. 58RE Ch. 5 - Prob. 59RE Ch. 5 - Prob. 60RE Ch. 5 - Prob. 61RE Ch. 5 - Prob. 62RE Ch. 5 - Prob. 63RE Ch. 5 - Personal Finance Carla Truss owes $5800 to her...Ch. 5 - Business Financing Candice Cotton needs to borrow...Ch. 5 - Prob. 66RE Ch. 5 - Business Investment A developer deposits $84,720...Ch. 5 - Prob. 68RE Ch. 5 - Prob. 69RE Ch. 5 - Prob. 70RE Ch. 5 - Prob. 71RE Ch. 5 - Prob. 72RE Ch. 5 - Business Financing The owner of Eastside Hallmark...Ch. 5 - Personal Finance To buy a new computer, David Berg...Ch. 5 - Prob. 75RE Ch. 5 - Prob. 76RE Ch. 5 - Prob. 77RE Ch. 5 - 78. New Car In Spring 2014, some dealers...Ch. 5 - Buying and Selling a House The Bahary family...Ch. 5 - Prob. 80RE Ch. 5 - Prob. 81RE

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

Why the present value of perpetuity is given by P = R i ?

Solution Summary: The author explains that a perpetuity is an annuity in which the payments go on forever.

Concept explainers

Videos

Why the present value of perpetuity is given by P=Ri?

Want to see the full answer?

Chapter 5 Solutions