A principal value of 200 is invested for one year: (i) The return rate over the year is estimated to be increasing linearly from0.10to0.14.Inthiscaset =0.04t+0.1.Findthecumulativeinterest

A principal value of 200 is invested for one year:

(i) The return rate over the year is estimated to be increasing linearly from0.10to0.14.Inthiscaseγt =0.04t+0.1.Findthecumulativeinterest rate, rate function, future value.

(ii) The mean of the financial rate is defined by the integrable function γ_u =0.04u + 0.10 while the variance is γ_u =0.002(1 + 0.001u). Find the expectation of rate function and the expected future value.