During the first 4 years, interest is credited using a simple interest of 5% per year. After 4 years, interest is credited at a force of interest

The following are numerically equal:

(i) The value at time t = 4 of payments of 1000 at time t = 2 and 400 at time t = 7

(ii) The present value at time t = 0 of a payment of X at time t = 10

Calculate X.

0.2 ,t 4 1+0.2