Explanation Given: Future income stream is F V ( t ) = 5000 + 500 t over next 10 years at an interest of 2 % compounded continuously. Formula used: The present value of the single future payment described will be: P V = F V ( t ) ⋅ e − r t Here, P V is present value, r is rate of interest and t is time in years. Calculation: Recall the present value formula of the single future payment. P V = F V ( t ) ⋅ e − r t Here, P V is present value, r is rate of interest and t is time in years. The payment is to be made over 10 y e a r s , hence a definite integral is to done from t = 0 to t = 10 P V = ∫ t = 0 t = 10 F V ( t ) ⋅ e − r t d t Substitute 5000 + 500 t for F V ( t ) , 0.02 for r and integrate. P V = ∫ t = 0 t = 10 5000 + 500 t ⋅ e − 0.02 t d t Apply integration by parts and consider u = 5000 + 500 t and d v = e − 0.02 t d t which will provide following. d u = 500 d t and, d v = e − 0.02 t d t t v = e − 0.02 t − 0.02 Consider integration by parts. P V = ∫ t = 0 t = 10 ( 5000 + 500 t ) ⋅ e − 0.02 t d t = v u | t = 0 t = 10 − ∫ t = 0 t = 10 v d u = ( ( 5000 + 500 t ) e − 0

Mathematics With Applications, Loose-leaf Edition Plus Mylab Math With Pearson Etext -- 18-week Access Card Package (12th Edition)

12th Edition

ISBN: 9780135998304

Author: Margaret L. Lial, Tom Hungerford, John P. Holcomb, Bernadette Mullins

Publisher: PEARSON

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 13.6, Problem 35E

To determine

Present value of the income to fund a future income stream of FV(t)=5000+500t over next 10 years at an interest of 2% compounded continuously.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.6, Problem 34E

Chapter 13.6, Problem 36E

Students have asked these similar questions

= 1. Show (a) Let G = Z/nZ be a cyclic group, so G = {1, 9, 92,...,g" } with g": that the group algebra KG has a presentation KG = K(X)/(X” — 1). (b) Let A = K[X] be the algebra of polynomials in X. Let V be the A-module with vector space K2 and where the action of X is given by the matrix Compute End(V) in the cases (i) x = p, (ii) xμl. (67) · (c) If M and N are submodules of a module L, prove that there is an isomorphism M/MON (M+N)/N. (The Second Isomorphism Theorem for modules.) You may assume that MON is a submodule of M, M + N is a submodule of L and the First Isomorphism Theorem for modules.

(a) Define the notion of an ideal I in an algebra A. Define the product on the quotient algebra A/I, and show that it is well-defined. (b) If I is an ideal in A and S is a subalgebra of A, show that S + I is a subalgebra of A and that SnI is an ideal in S. (c) Let A be the subset of M3 (K) given by matrices of the form a b 0 a 0 00 d Show that A is a subalgebra of M3(K). Ꮖ Compute the ideal I of A generated by the element and show that A/I K as algebras, where 0 1 0 x = 0 0 0 001

(a) Let HI be the algebra of quaternions. Write out the multiplication table for 1, i, j, k. Define the notion of a pure quaternion, and the absolute value of a quaternion. Show that if p is a pure quaternion, then p² = -|p|². (b) Define the notion of an (associative) algebra. (c) Let A be a vector space with basis 1, a, b. Which (if any) of the following rules turn A into an algebra? (You may assume that 1 is a unit.) (i) a² = a, b²=ab = ba 0. (ii) a² (iii) a² = b, b² = abba = 0. = b, b² = b, ab = ba = 0. (d) Let u1, 2 and 3 be in the Temperley-Lieb algebra TL4(8). ገ 12 13 Compute (u3+ Augu2)² where A EK and hence find a non-zero x € TL4 (8) such that ² = 0.

Chapter 13 Solutions

Mathematics With Applications, Loose-leaf Edition Plus Mylab Math With Pearson Etext -- 18-week Access Card Package (12th Edition)

Ch. 13.1 - Checkpoint 1 Find an antiderivative for each of...Ch. 13.1 - Checkpoint 2 Find each of the...Ch. 13.1 - Prob. 3CP Ch. 13.1 - Prob. 4CP Ch. 13.1 - Prob. 5CP Ch. 13.1 - Prob. 6CP Ch. 13.1 - Prob. 7CP Ch. 13.1 - Checkpoint 8 The marginal cost at a level of...Ch. 13.1 - 1. What must be true of F(x) and G(x) if both are...Ch. 13.1 - 2. How is the antiderivative of a function related...

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.

Present value of the income to fund a future income stream of F V ( t ) = 5000 + 500 t over next 10 years at an interest of 2 % compounded continuously.

Solution Summary: The author explains the present value of the income to fund a future income stream of FV(t)=5000+500t over next 10 years.

Concept explainers

Videos

Present value of the income to fund a future income stream of FV(t)=5000+500t over next 10 years at an interest of 2% compounded continuously.

Want to see the full answer?

Chapter 13 Solutions