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* The force of interest 8(t) at time t (measured in years) is a +bt² where a and b are constants. 0 accumulates to £210 at t = 5 and £230 at t = = 10. An amount of £200 at time t = (a) Show that a = log (1.05) -log(1.15) = 0.008352, b = 20 log(1.15) - 125 log (1.05) = 0.0001687. and (b) Compute A(0,7) and hence compute the discounted value at t = £750 due at t = 7. 0 of a payment of (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. 0 accumulates to £210 at t = 5 and £230 at t = = 10. An amount of £200 at time t = (a) Show that a = log (1.05) -log(1.15) = 0.008352, b = 20 log(1.15) - 125 log (1.05) = 0.0001687. and (b) Compute A(0,7) and hence compute the discounted value at t = £750 due at t = 7. 0 of a payment of (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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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* The force of interest 8(t) at time † (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 f = 10. (a) Show that = = a = b = 2log (1.15) - 125 log (1.05) log (1.05)-log(1.15) = 0.008352, 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. = = and (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.
Transcribed Image Text:* The force of interest 8(t) at time † (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 f = 10. (a) Show that = = a = b = 2log (1.15) - 125 log (1.05) log (1.05)-log(1.15) = 0.008352, 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. = = and (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.
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