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 and £230 at t = 10. = 0 accumulates to £210 at t = 5 (a) Show that 1 4 a = 15 1 b = 250 log (1.05) log (1.15) - 3 log(1.15) 0.008352, 1 125 = 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.
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 and £230 at t = 10. = 0 accumulates to £210 at t = 5 (a) Show that 1 4 a = 15 1 b = 250 log (1.05) log (1.15) - 3 log(1.15) 0.008352, 1 125 = 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.
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
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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
and £230 at t = 10.
=
0 accumulates to £210 at t = 5
(a) Show that
1
4
a =
15
1
b =
250
log (1.05)
log (1.15) -
3
log(1.15) 0.008352,
1
125
=
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.
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