$1\mathrm{.}6\mathrm{.}3$S At time $t=0,1$ is deposited into each of Fund $x$ and Fund $Y.$

Fund $x$ accumulates at a force of interest ${}_t=\frac{t^2}{k}.$ Fund $Y$ accu$-$

mulates at a nominal rate of discount of $8\%$ per annum converti$-$

ble semiannually. At time $t=5,$ the accumulated value of Fund $x$

equals the accumulated value of Fund $Y.$ Determine $k.$