Calculate the effective annual interest rate for the following: a. A 3-month T-bill selling at $97,820 with par value $100,000. (Round your answers to 2 decimal places.) b. A 8% coupon bond selling at par and paying coupons semiannually.

A.9.2%

B.8.16%

Explanation:

a. Calculation for the Effective annual rate on three-month T-bill

First step

T-bill =(Par value-Selling amount)/Par value

Let plug in the formula

T-bill =($100,000-$97,820)/$97,820

T-bill =$2,180/$97,820

T-bill =0.02228

Now let calculate for the Effective Annual Interest rate

Effective Annual Interest rate = (1 + 0.02228)^4– 1

Effective Annual Interest rate = (1.02228)^4-1

Effective Annual Interest rate =1.0921-1

Effective Annual Interest rate =0.0921×100

Effective Annual Interest rate=9.2%

B. Calculation for the effective annual interest rate for A 8% coupon bond .

First step

Semi-annual return=8%/2

Semi-annual return=4%

Second step is to calculate for the effective annual interest rate

Using this formula

Effective annual interest rate =(1+Semi-annual return percentage)^2-1

Let plug in the formula

Effective annual interest rate=(1+0.04)^2-1

Effective annual interest rate=(1.04)^2-1

Effective annual interest rate=1.0816-1

Effective annual interest rate=0.0816×100

Effective annual interest rate=8.16%

Therefore the Effective annual rate on three-month T-bill will be 9.2% while that of coupon bond is 8.16%

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