Future Value: If the company deposits $$2$ million in a bank account that pays $6\%$ interest annually, how much will be in the account after $5$ years?

Present Value: What is the present value of a security that will pay $$29,000$ in $20$ years if securities of equal risk pay $5\%$ annually?

Required Interest Rates: The company owner has said she will retire in $19$ years. She currently has $$350,000$ saved and thinks she will need $$800,000$ at retirement. What annual interest rate must she earn to reach that goal, assuming she does not save any additional funds?

Future Value of an Annuity: Find the future values of these ordinary annuities. Compounding occurs once a year.

$$500$ per year for $8$ years at $14\%$

$$250$ per year for $4$ years at $7\%$

$$700$ per year for $4$ years at $0\%$

Present Value of an Annuity: Find the present values of these ordinary annuities. Discounting occurs once a year.

$$600$ per year for $12$ years at $8\%$

$$300$ per year for $6$ years at $4\%$

$$500$ per year for $6$ years at $0\%$

Bond Valuation: The company has two bonds in their investment portfolio, Bond C and Bond Z$.$ Each bond matures in $4$ years, has a face value of $$1,000,$ and has a yield to maturity of $8\mathrm{.}2\%.$ Bond C pays an $11\mathrm{.}5\%$ annual coupon, while Bond Z is a zero$-$coupon bond.

Assuming that the yield to maturity of each bond remains at $8\mathrm{.}2\%$ over the next $4$ years, calculate the price of the bonds at each of the following years to maturity. Explain any observed differences from the pricing calculations of the two bonds.

Years to Maturity Price of Bond C Price of Bond Z

$4$

$3$

$2$

$1$

$0$

Yield to Maturity and Yield to Call: The owner is interested in investing some retained earnings in corporate bonds. She is considering the following:

Bond A has a $7\%$ annual coupon, matures in $12$ years, and has a $$1,000$ face value.

Bond B has a $9\%$ annual coupon, matures in $12$ years, and has a $$1,000$ face value.

Bond C has an $11\%$ annual coupon, matures in $12$ years, and has a $$1,000$ face value.

Each bond has a yield to maturity of $9\%.$

a$.$ Before calculating the prices of the bonds, identify whether each bond is trading at a premium, at a discount, or at par.

b$.$ Calculate the price of each of the three bonds.

c$.$ Calculate the current yield for each of the three bonds.