$(2$ points$)$ Suppose that Fund I has a force of interest given by ${}_t=\frac{0\mathrm{.}06}{1+\mathrm{.}03t}.$

a$)$ Find $a(t)$ for Fund I.

b$)$ Suppose that Fund II pays a nominal rate of interest at a rate of $5\mathrm{.}2\%$

compounded quarterly. Find the values of $t$ where ${}_t$ for Fund I and Fund II

have the same value.