During the first $3$ years, interest is credited using a compound interest rate of $4\%$ per year. After $3$ years,

interest is credited at a force of interest:

${}_t=\frac{0\mathrm{.}1}{1+0\mathrm{.}1t},t3$

The following are numerically equal

the current value at time $t=3$ of payment of $1000$ at time $t=2$ and $500$ at time $t=6$; and

the present value at time $t=0$ of a payment of $x$ at time $t=10.$

Calculate $x$