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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 1 a = log (1.05) log(1.15) = 0.008352, and b = - 250 log(1.15) 15 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 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 1 a = log (1.05) log(1.15) = 0.008352, and b = - 250 log(1.15) 15 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.

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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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 1 a = log (1.05) log(1.15) = 0.008352, and b = - 250 log(1.15) 15 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.
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 1 a = log (1.05) log(1.15) = 0.008352, and b = - 250 log(1.15) 15 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.
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