3. * The force of interest (t) at time t (measured in years) is a + bt² where a and b are constants. An amount of £200 at time t = 0 accumulates to £210 at t = 5 and £230 at t = 10. 1 (a) Show that a = log (1.05) - 30 log(1.15) = 0.008352, and b = 250 log(1.15) - 125 log(1.05) = 0.0001687. (b) Compute A(0, 7) and hence compute the discounted value at t = 0 of a payment of £750 due at t = 7. (c) Compute A(6, 7). What is the equivalent constant annual interest rate for the year from t = 6 to t = 7? (d) Calculate the constant force of interest that would give rise to the same accumulation from t = 0 to t = 10.
3. * The force of interest (t) at time t (measured in years) is a + bt² where a and b are constants. An amount of £200 at time t = 0 accumulates to £210 at t = 5 and £230 at t = 10. 1 (a) Show that a = log (1.05) - 30 log(1.15) = 0.008352, and b = 250 log(1.15) - 125 log(1.05) = 0.0001687. (b) Compute A(0, 7) and hence compute the discounted value at t = 0 of a payment of £750 due at t = 7. (c) Compute A(6, 7). What is the equivalent constant annual interest rate for the year from t = 6 to t = 7? (d) Calculate the constant force of interest that would give rise to the same accumulation from t = 0 to t = 10.
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
Related questions
Question
Transcribed Image Text:3. * The force of interest (t) at time t (measured in years) is a + bt² where a and
b are constants. An amount of £200 at time t = 0 accumulates to £210 at t = 5
and £230 at t = 10.
1
(a) Show that
a = log (1.05)
-
30
log(1.15)
= 0.008352,
and
b
=
250 log(1.15)
-
125
log(1.05) = 0.0001687.
(b) Compute A(0, 7) and hence compute the discounted value at t = 0 of a
payment of £750 due at t = 7.
(c) Compute A(6, 7). What is the equivalent constant annual interest rate for
the year from t = 6 to t = 7?
(d) Calculate the constant force of interest that would give rise to the same
accumulation from t = 0 to t = 10.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
Essentials Of Investments
Finance
ISBN:
9781260013924
Author:
Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:
Mcgraw-hill Education,
Essentials Of Investments
Finance
ISBN:
9781260013924
Author:
Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:
Mcgraw-hill Education,
Foundations Of Finance
Finance
ISBN:
9780134897264
Author:
KEOWN, Arthur J., Martin, John D., PETTY, J. William
Publisher:
Pearson,
Fundamentals of Financial Management (MindTap Cou…
Finance
ISBN:
9781337395250
Author:
Eugene F. Brigham, Joel F. Houston
Publisher:
Cengage Learning
Corporate Finance (The Mcgraw-hill/Irwin Series i…
Finance
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