3. * The force of interest (t) at time t (measured in years) is a +...

 

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3. * The force of interest (t) at time t (measured in years) is a + bt 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, log(1.15) 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 6 to 7? (d) Calculate the constant force of interest that would give rise to the same accumulation from 0 tot 10. 3. * The force of interest (t) at time t (measured in years) is a + bt 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, log(1.15) 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 6 to 7? (d) Calculate the constant force of interest that would give rise to the same accumulation from 0 tot 10.