You will receive $$100$ from a savings bond in $2$ years. The nominal interest rate is $7\mathrm{.}10\%.$

a$.$ What is the present value of the proceeds from the bond?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

b$.$ If the inflation rate over the next few years is expected to be $2\mathrm{.}10\%,$ what will the real value of the $$100$ payoff be in terms of

today's dollars?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

c$.$ What is the real interest rate?

Note: Do not round intermediate calculations. Enter your answer as a percent rounded to $2$ decimal places.

d$.$ Calculate the real payoff from the bond $[$from part $($b$)]$ discounted at the real interest rate $[$from part $($c$)].$

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.