* The force of interest 8(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. (a) Show that a = b= log (1.05)-log(1.15) = 0.008352, 250 log (1.15)-15 log (1.05) = 0.0001687. and (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.
* The force of interest 8(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. (a) Show that a = b= log (1.05)-log(1.15) = 0.008352, 250 log (1.15)-15 log (1.05) = 0.0001687. and (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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:3. * The force of interest 8(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.
(a) Show that
a =
b =
log (1.05)-log(1.15) = 0.008352,
250 log (1.15) 15 log (1.05) = 0.0001687.
-
and
(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 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.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
