Explanation Theorem used: If | r | < 1 , then the geometric series ∑ n = 0 ∞ a r n = a + a r + a r 2 + ⋯ converges and it sum is a 1 − r ; that is, ∑ n = 0 ∞ a r n = a + a r + a r 2 + ⋯ = a 1 − r . The series diverges if | r | ≥ 1 . Calculation: The capital value of perpetuity A is the sum of the present values of the payments at the end of each investment period. The present value of the amount of the first payment is P e − r ( 1 ) . The present value of the amount of the second payment is P e − r ( 2 ) . Similarly, the present value of the amount of the n th payment that compounded continuously is P e − r n . The capital value of the perpetuity is calculated by using the above mentioned theorem as follows

10th Edition

ISBN: 9781337825597

Author: Tan

Publisher: INTER CENG

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 11.3, Problem 41E

To determine

To find: A formula for the capital value of a perpetuity involving payments of P dollars paid at the end of each investment period into a fund that earns interest at the rate of r% year compounded continuously.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.3, Problem 40E

Chapter 11.3, Problem 42E

Students have asked these similar questions

Two cables tied together at C are loaded as shown. Given: Q = 130 lb. 8 30° C B Q 3 4 Draw the free-body diagram needed to determine the range of values of P for which both cables remain taut.

Cable AB is 103 ft long and the tension in the cable is 3900 lb. 56 ft A 50° 20° B x C Identify the angles 0.0, and 8, that define the direction of force. 1 By N 2 Match each of the options above to the items below. 142.1° 57.1° 73.3° 3 8.

In the given figure, P = 51 lb . 65° C 25° 35° 75 lb P Determine the corresponding magnitude of the resultant. The corresponding magnitude of the resultant is| lb.

Chapter 11 Solutions

APP CAL MANAGE,LIFE,SOC STUD WEB ASSIGN

Ch. 11.1 - Prob. 1CQ Ch. 11.1 - Prob. 2CQ Ch. 11.1 - Prob. 1E Ch. 11.1 - In Exercises 110, find the first three Taylor...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E

Ch. 11.1 - In Exercises 110, find the first three Taylor...Ch. 11.1 - Prob. 10E Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - In Exercises 1120, find the nth Taylor polynomial...Ch. 11.1 - Prob. 16E Ch. 11.1 - Prob. 17E Ch. 11.1 - Prob. 18E Ch. 11.1 - Prob. 19E Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Prob. 31E Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.1 - Let f(x) = ex. a. Find a bound in the error...Ch. 11.1 - Prob. 36E Ch. 11.1 - Prob. 37E Ch. 11.1 - Prob. 38E Ch. 11.1 - Prob. 39E Ch. 11.1 - Prob. 40E Ch. 11.1 - Prob. 41E Ch. 11.1 - According to a joint study conducted by Oxnards...Ch. 11.1 - Prob. 43E Ch. 11.1 - Prob. 44E Ch. 11.1 - Prob. 45E Ch. 11.1 - Prob. 46E Ch. 11.2 - Prob. 1CQ Ch. 11.2 - Prob. 1E Ch. 11.2 - Prob. 2E Ch. 11.2 - Prob. 3E Ch. 11.2 - Prob. 4E Ch. 11.2 - Prob. 5E Ch. 11.2 - Prob. 6E Ch. 11.2 - Prob. 7E Ch. 11.2 - Prob. 8E Ch. 11.2 - Prob. 9E Ch. 11.2 - Prob. 10E Ch. 11.2 - Prob. 11E Ch. 11.2 - In Exercises 1021, find the nth term of the...Ch. 11.2 - Prob. 13E Ch. 11.2 - Prob. 14E Ch. 11.2 - Prob. 15E Ch. 11.2 - Prob. 16E Ch. 11.2 - Prob. 17E Ch. 11.2 - Prob. 18E Ch. 11.2 - Prob. 19E Ch. 11.2 - Prob. 20E Ch. 11.2 - Prob. 21E Ch. 11.2 - Prob. 22E Ch. 11.2 - Prob. 23E Ch. 11.2 - Prob. 24E Ch. 11.2 - Prob. 25E Ch. 11.2 - Prob. 26E Ch. 11.2 - Prob. 27E Ch. 11.2 - Prob. 28E Ch. 11.2 - Prob. 29E Ch. 11.2 - Prob. 30E Ch. 11.2 - Prob. 31E Ch. 11.2 - Prob. 32E Ch. 11.2 - Prob. 33E Ch. 11.2 - Prob. 34E Ch. 11.2 - Prob. 35E Ch. 11.2 - Prob. 36E Ch. 11.2 - Prob. 37E Ch. 11.2 - Prob. 38E Ch. 11.2 - Prob. 39E Ch. 11.2 - Prob. 40E Ch. 11.2 - Prob. 41E Ch. 11.2 - Prob. 42E Ch. 11.2 - Prob. 43E Ch. 11.2 - Prob. 44E Ch. 11.2 - Prob. 45E Ch. 11.2 - Prob. 46E Ch. 11.2 - Prob. 47E Ch. 11.2 - Prob. 48E Ch. 11.2 - Prob. 49E Ch. 11.2 - Prob. 50E Ch. 11.2 - Prob. 51E Ch. 11.2 - Prob. 52E Ch. 11.3 - Prob. 1CQ Ch. 11.3 - Prob. 2CQ Ch. 11.3 - Prob. 1E Ch. 11.3 - Prob. 2E Ch. 11.3 - Prob. 3E Ch. 11.3 - Prob. 4E Ch. 11.3 - Prob. 5E Ch. 11.3 - Prob. 6E Ch. 11.3 - Prob. 7E Ch. 11.3 - Prob. 8E Ch. 11.3 - Prob. 9E Ch. 11.3 - Prob. 10E Ch. 11.3 - Prob. 11E Ch. 11.3 - Prob. 12E Ch. 11.3 - Prob. 13E Ch. 11.3 - Prob. 14E Ch. 11.3 - Prob. 15E Ch. 11.3 - Prob. 16E Ch. 11.3 - Prob. 17E Ch. 11.3 - Prob. 18E Ch. 11.3 - Prob. 19E Ch. 11.3 - Prob. 20E Ch. 11.3 - Prob. 21E Ch. 11.3 - Prob. 22E Ch. 11.3 - Prob. 23E Ch. 11.3 - Prob. 24E Ch. 11.3 - Prob. 25E Ch. 11.3 - Prob. 26E Ch. 11.3 - Prob. 27E Ch. 11.3 - Prob. 28E Ch. 11.3 - Prob. 29E Ch. 11.3 - Prob. 30E Ch. 11.3 - Prob. 31E Ch. 11.3 - Prob. 32E Ch. 11.3 - Prob. 33E Ch. 11.3 - Prob. 34E Ch. 11.3 - Prob. 35E Ch. 11.3 - Prob. 36E Ch. 11.3 - Prob. 37E Ch. 11.3 - Prob. 38E Ch. 11.3 - Prob. 39E Ch. 11.3 - Prob. 40E Ch. 11.3 - Prob. 41E Ch. 11.3 - Prob. 42E Ch. 11.3 - Suppose that a dose of C units of a certain drug...Ch. 11.3 - Prob. 44E Ch. 11.3 - In Exercises 4548, determine whether the statement...Ch. 11.3 - Prob. 46E Ch. 11.3 - Prob. 47E Ch. 11.3 - Prob. 48E Ch. 11.4 - Prob. 1CQ Ch. 11.4 - Prob. 2CQ Ch. 11.4 - Prob. 3CQ Ch. 11.4 - Prob. 1E Ch. 11.4 - Prob. 2E Ch. 11.4 - Prob. 3E Ch. 11.4 - Prob. 4E Ch. 11.4 - Prob. 5E Ch. 11.4 - Prob. 6E Ch. 11.4 - Prob. 7E Ch. 11.4 - Prob. 8E Ch. 11.4 - Prob. 9E Ch. 11.4 - Prob. 10E Ch. 11.4 - Prob. 11E Ch. 11.4 - Prob. 12E Ch. 11.4 - Prob. 13E Ch. 11.4 - Prob. 14E Ch. 11.4 - Prob. 15E Ch. 11.4 - Prob. 16E Ch. 11.4 - Prob. 17E Ch. 11.4 - Prob. 18E Ch. 11.4 - Prob. 19E Ch. 11.4 - Prob. 20E Ch. 11.4 - Prob. 21E Ch. 11.4 - Prob. 22E Ch. 11.4 - Prob. 23E Ch. 11.4 - Prob. 24E Ch. 11.4 - Prob. 25E Ch. 11.4 - Prob. 26E Ch. 11.4 - Prob. 27E Ch. 11.4 - Prob. 28E Ch. 11.4 - Prob. 29E Ch. 11.4 - Prob. 30E Ch. 11.4 - Prob. 31E Ch. 11.4 - Prob. 32E Ch. 11.4 - Prob. 33E Ch. 11.4 - Prob. 34E Ch. 11.4 - Prob. 35E Ch. 11.4 - Prob. 36E Ch. 11.4 - Prob. 37E Ch. 11.4 - Prob. 38E Ch. 11.4 - Prob. 39E Ch. 11.4 - Prob. 40E Ch. 11.4 - Prob. 41E Ch. 11.4 - Prob. 42E Ch. 11.4 - Prob. 43E Ch. 11.4 - Prob. 44E Ch. 11.4 - Prob. 45E Ch. 11.4 - Prob. 46E Ch. 11.4 - Prob. 47E Ch. 11.4 - Prob. 48E Ch. 11.4 - Prob. 49E Ch. 11.4 - Prob. 50E Ch. 11.4 - Prob. 51E Ch. 11.4 - Prob. 52E Ch. 11.4 - Prob. 53E Ch. 11.4 - Prob. 54E Ch. 11.4 - Prob. 55E Ch. 11.4 - Prob. 56E Ch. 11.4 - Prob. 57E Ch. 11.4 - Prob. 58E Ch. 11.4 - Prob. 59E Ch. 11.4 - Prob. 60E Ch. 11.5 - Prob. 1CQ Ch. 11.5 - a. What is the radius of convergence of a power...Ch. 11.5 - Prob. 3CQ Ch. 11.5 - Prob. 4CQ Ch. 11.5 - Prob. 5CQ Ch. 11.5 - Prob. 1E Ch. 11.5 - Prob. 2E Ch. 11.5 - Prob. 3E Ch. 11.5 - Prob. 4E Ch. 11.5 - Prob. 5E Ch. 11.5 - Prob. 6E Ch. 11.5 - Prob. 7E Ch. 11.5 - Prob. 8E Ch. 11.5 - Prob. 9E Ch. 11.5 - Prob. 10E Ch. 11.5 - Prob. 11E Ch. 11.5 - Prob. 12E Ch. 11.5 - Prob. 13E Ch. 11.5 - Prob. 14E Ch. 11.5 - Prob. 15E Ch. 11.5 - Prob. 16E Ch. 11.5 - Prob. 17E Ch. 11.5 - Prob. 18E Ch. 11.5 - Prob. 19E Ch. 11.5 - Prob. 20E Ch. 11.5 - Prob. 21E Ch. 11.5 - Prob. 22E Ch. 11.5 - Prob. 23E Ch. 11.5 - Prob. 24E Ch. 11.5 - Prob. 25E Ch. 11.5 - Prob. 26E Ch. 11.5 - Prob. 27E Ch. 11.5 - Prob. 28E Ch. 11.5 - Prob. 29E Ch. 11.5 - Prob. 30E Ch. 11.5 - Prob. 31E Ch. 11.5 - Prob. 32E Ch. 11.5 - Prob. 33E Ch. 11.5 - Prob. 34E Ch. 11.5 - Prob. 35E Ch. 11.5 - Prob. 36E Ch. 11.6 - Prob. 1CQ Ch. 11.6 - Prob. 2CQ Ch. 11.6 - Prob. 3CQ Ch. 11.6 - Prob. 1E Ch. 11.6 - Prob. 2E Ch. 11.6 - Prob. 3E Ch. 11.6 - Prob. 4E Ch. 11.6 - Prob. 5E Ch. 11.6 - Prob. 6E Ch. 11.6 - Prob. 7E Ch. 11.6 - Prob. 8E Ch. 11.6 - Prob. 9E Ch. 11.6 - Prob. 10E Ch. 11.6 - Prob. 11E Ch. 11.6 - Prob. 12E Ch. 11.6 - Prob. 13E Ch. 11.6 - Prob. 14E Ch. 11.6 - Prob. 15E Ch. 11.6 - Prob. 16E Ch. 11.6 - Prob. 17E Ch. 11.6 - Prob. 18E Ch. 11.6 - Prob. 19E Ch. 11.6 - Prob. 20E Ch. 11.6 - Prob. 21E Ch. 11.6 - Prob. 22E Ch. 11.6 - Prob. 23E Ch. 11.6 - Prob. 24E Ch. 11.6 - Prob. 25E Ch. 11.6 - Prob. 26E Ch. 11.6 - Prob. 27E Ch. 11.6 - Prob. 28E Ch. 11.6 - Prob. 29E Ch. 11.6 - Prob. 30E Ch. 11.6 - Prob. 31E Ch. 11.6 - Prob. 32E Ch. 11.7 - Prob. 1CQ Ch. 11.7 - Prob. 2CQ Ch. 11.7 - Prob. 3CQ Ch. 11.7 - Prob. 1E Ch. 11.7 - Prob. 2E Ch. 11.7 - Prob. 3E Ch. 11.7 - Prob. 4E Ch. 11.7 - Prob. 5E Ch. 11.7 - Prob. 6E Ch. 11.7 - Prob. 7E Ch. 11.7 - Prob. 8E Ch. 11.7 - Prob. 9E Ch. 11.7 - Prob. 10E Ch. 11.7 - Prob. 11E Ch. 11.7 - Prob. 12E Ch. 11.7 - Prob. 13E Ch. 11.7 - Prob. 14E Ch. 11.7 - Prob. 15E Ch. 11.7 - Prob. 16E Ch. 11.7 - Prob. 17E Ch. 11.7 - Prob. 18E Ch. 11.7 - Prob. 19E Ch. 11.7 - Prob. 20E Ch. 11.7 - Prob. 21E Ch. 11.7 - Prob. 22E Ch. 11.7 - In Exercises 2328, make a rough sketch of the...Ch. 11.7 - Prob. 24E Ch. 11.7 - Prob. 25E Ch. 11.7 - Prob. 26E Ch. 11.7 - Prob. 27E Ch. 11.7 - Prob. 28E Ch. 11.7 - Prob. 29E Ch. 11.7 - Prob. 30E Ch. 11.7 - Prob. 31E Ch. 11.7 - Prob. 32E Ch. 11.7 - Prob. 33E Ch. 11.7 - Prob. 34E Ch. 11.7 - Prob. 35E Ch. 11.7 - Prob. 36E Ch. 11.7 - Prob. 37E Ch. 11.7 - Prob. 38E Ch. 11.7 - Prob. 39E Ch. 11.7 - Prob. 40E Ch. 11.7 - Prob. 41E Ch. 11.7 - Prob. 1TE Ch. 11.7 - Prob. 2TE Ch. 11.7 - Prob. 3TE Ch. 11.7 - Prob. 4TE Ch. 11.7 - Prob. 5TE Ch. 11.7 - Prob. 6TE Ch. 11.7 - Prob. 7TE Ch. 11.7 - Prob. 8TE Ch. 11 - Prob. 1CRQ Ch. 11 - Prob. 2CRQ Ch. 11 - Prob. 3CRQ Ch. 11 - Prob. 4CRQ Ch. 11 - Prob. 5CRQ Ch. 11 - Prob. 6CRQ Ch. 11 - Prob. 7CRQ Ch. 11 - Prob. 8CRQ Ch. 11 - Prob. 9CRQ Ch. 11 - Prob. 10CRQ Ch. 11 - Prob. 1RE Ch. 11 - Prob. 2RE Ch. 11 - Prob. 3RE Ch. 11 - Prob. 4RE Ch. 11 - Prob. 5RE Ch. 11 - Prob. 6RE Ch. 11 - Prob. 7RE Ch. 11 - Prob. 8RE Ch. 11 - Prob. 9RE Ch. 11 - Prob. 10RE Ch. 11 - Prob. 11RE Ch. 11 - Prob. 12RE Ch. 11 - Prob. 13RE Ch. 11 - Prob. 14RE Ch. 11 - Prob. 15RE Ch. 11 - Prob. 16RE Ch. 11 - Prob. 17RE Ch. 11 - Prob. 18RE Ch. 11 - Prob. 19RE Ch. 11 - Prob. 20RE Ch. 11 - Prob. 21RE Ch. 11 - In Exercises 21 and 22, find the sum of the...Ch. 11 - Prob. 23RE Ch. 11 - Prob. 24RE Ch. 11 - Prob. 25RE Ch. 11 - Prob. 26RE Ch. 11 - Prob. 27RE Ch. 11 - Prob. 28RE Ch. 11 - Prob. 29RE Ch. 11 - Prob. 30RE Ch. 11 - Prob. 31RE Ch. 11 - Prob. 32RE Ch. 11 - Prob. 33RE Ch. 11 - Prob. 34RE Ch. 11 - Prob. 35RE Ch. 11 - Prob. 36RE Ch. 11 - Prob. 37RE Ch. 11 - Prob. 38RE Ch. 11 - Prob. 39RE Ch. 11 - Prob. 40RE Ch. 11 - Prob. 41RE Ch. 11 - Prob. 42RE Ch. 11 - Prob. 43RE Ch. 11 - Prob. 44RE Ch. 11 - Prob. 45RE Ch. 11 - Prob. 46RE Ch. 11 - Prob. 47RE Ch. 11 - Prob. 48RE Ch. 11 - Prob. 49RE Ch. 11 - Prob. 50RE Ch. 11 - Prob. 1BM Ch. 11 - Prob. 2BM Ch. 11 - Determine whether the series converges or...Ch. 11 - Prob. 4BM Ch. 11 - Prob. 5BM

Knowledge Booster

$Calculus$

Learn more about

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

A formula for the capital value of a perpetuity involving payments of P dollars paid at the end of each investment period into a fund that earns interest at the rate of r % year compounded continuously.

Concept explainers

Videos

To find: A formula for the capital value of a perpetuity involving payments of P dollars paid at the end of each investment period into a fund that earns interest at the rate of r% year compounded continuously.

Want to see the full answer?

Chapter 11 Solutions