Sam was injured in an accident, and the insurance company has offered him the choice of $$31,000$ per year for $15$ years, with the first payment being made today, or a lump sum. If a fair return is $7\mathrm{.}7\%,$ how large must the lump sum be to leave him as well off financially as with the annuity?

$$294,163\mathrm{.}77$

$$283,453\mathrm{.}58$

$$274,709\mathrm{.}39$

$$291,085\mathrm{.}51$

$$311,826\mathrm{.}54$

You agree to make $24$ deposits of $$500$ at the beginning of each month into a bank account. At interest monthly, what nominal annual interest rate will you be earning?

$4\mathrm{.}80\%$

$4\mathrm{.}37\%$

$5\mathrm{.}35\%$

$5\mathrm{.}41\%$

$3\mathrm{.}90\%$