Durning the first 4 years, interest is credited using a simple interest rate of 5% per year. After 4 years, interest is credited at a force of interest:
dell=0.2/(1+0.2t), t >=4.
The following are numerically equal:
i) the current value at time t=4 of payments of 1000 at time t=2 and
400 at time t=7; and
ii) the present value at time t=0 of a payment of X at time t=10.
Calculate X.