Q$3.$ a$)$ A $$10,000,12\%$ bond maturing in $10$ years with interest paid quarterly is offered for

sale for $ $8,021.$ If the market rate of interest is compounded quarterly, what is the effective

annual rate earned? What is the nominal interest rate earned? What is the effective annual rate

earned?

b$)$ If the inflation rate is $2\%$ per quarter, what equal$-$payment series for $40$ quarters in terms of

constant dollars is equivalent to the interest payments of $$300$ per quarter to be received from

the bond? What is the constant$-$dollar value of the par value of the bond received at maturity?

What is the present equivalent value of the bond when inflation is considered? Calculate the

effective inflation$-$free interest rate being earned by this bond for the given rate of inflation.

Compare these values to those in part $($a$).$