3. The force of interest (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=154log(1.05)301log(1.15)=0.008352,andb=2501log(1.15)1251log(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