Question $5\mathrm{.}22$

Steve will receive $$100$ in $3$ years. Over the next three years, the interest rates will vary

as follows:

In the first year, the nominal discount rate is $6\%$ compounded monthly.

In the second year, the nominal interest rate is $7\%$ compounded quarterly.

In the third year, the constant annual force of interest is $10\%.$

Calculate the present value at time $0$ of the $$100$ payment.

A $79\mathrm{.}49$

B $79\mathrm{.}86$

C $80\mathrm{.}21$

D $84\mathrm{.}38$

E $89\mathrm{.}65$

The answer should be A$.79\mathrm{.}49.$ Please solve by hand.