A person$$s savings earns an effective annual rate of return of $12\%.$ Income tax is paid on the interest earned at a rate of $40\%.$ If the inflation rate is $5\%$ per year, what is the annual after$-$tax real rate of return?

Problem #$4$:

What is the price $P$ today of a $$80,000182-$day Canadian T$-$Bill if its quoted yield is $10\mathrm{.}08\%?$

Problem #$4$:

Answer correct to $2$ decimals.

Submit Problem #$4$ for Grading

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Problem #$5$:

Find $\frac{dP}{di},$ the derivative of the previous result from Problem #$4$ above, with respect to the quoted yield $i.$ Use this derivative to approximate the change in the price of the $T$ Bill if the yield were to have decreased by $0\mathrm{.}002($i$.$e$.0\mathrm{.}2\%)$ immediately after the T$-$Bill was purchased.

Problem #$5$:

Answer correct to $2$ decimals.

Submit Problem #$5$ for Grading

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