APPENDIX c

Time Value of Money

Calculate the future value of a single amount(LO2)

EC–1The four people below have the following investments.

Invested Amount / Interest Rate / Compounding
Jerry / $14,000 / 8% / Quarterly
Elaine / 16,000 / 6 / Semi-annually
George / 21,000 / 9 / Annually
Kramer / 19,000 / 7 / Annually

Required:

Determine which of the four people will have the greatest investment accumulation in four years.

Calculate the future value of a single amount(LO2)

EC–2You want to save for retirement. Assuming you are now 20 years old and you want to retire at age 60, you have 40 years to watch your investment grow. You decide to invest in the stock market, which has earned about 12% per year over the past 80 years and is expected to continue at this rate. You decide to invest $2,000 today.

Required:

How much do you expect to have in 40 years?

Calculate the present value of a single amount(LO2)

EC–3The four actors below have just signed a contract to star in a dramatic movie about relationships among hospital doctors. Each person signs independent contracts with the following terms:

Contract Terms
Contract Amount / Payment Date
Derek / $680,000 / Today
Isabel / 740,000 / 1 years
Meredith / 750,000 / 2 years
George / 820,000 / 3 year

Required:

Assuming an annual discount rate of 10%, which of the four actors is actually being paid the most?

Calculate the present value of a single amount(LO2)

EC–4Ray and Rachel are considering the purchase of two deluxe kitchen ovens. The first store offers the two ovens for $3,000 with payment due today. The second store offers the two ovens for $3,600 due in two years.

Required:

Assuming an annual discount rate of 10%, from which store should Ray and Rachel buy their ovens?

Calculate the present value of a single amount(LO2)

EC–5Lights, Camera, and More sells filmmaking equipment. The company offers three purchase options: (1) pay full cash today, (2) pay one-half down and the remaining one-half plus 8% in one year, or (3) pay nothing down and the full amount plus 9% in one year. George is considering buying equipment from Lights, Camera, and More for $80,000 and therefore has the following payment options:

Payment Today / Payment in One Year / Total Payment
Option 1 / $80,000 / $ 0 / $80,000
Option 2 / 40,000 / 43,200 / 83,200
Option 3 / 0 / 87,200 / 87,200

Required:

Assuming an annual discount rate of 12%, calculate which option has the lowest total cost in present value terms.

Calculate the future value of an annuity(LO3)

EC–6GMG Studios plans to invest $70,000 at the end of each year for the next five years. There are three investment options available.

Annual Rate / Interest Compounded / Period Invested
Option 1 / 5% / Annually / 5 years
Option 2 / 7 / Annually / 5 years
Option 3 / 9 / Annually / 5 years

Required:

Determine the accumulated investment amount by the end of the fifth year for each of the options.

Calculate the future value of an annuity(LO3)

EC–7You would like to start saving for retirement. Assuming you are now 20 years old and you want to retire at age 60, you have 40 years to watch your investment grow. You decide to invest in the stock market, which has earned about 12% per year over the past 80 years and is expected to continue at this rate. You decide to invest $2,000 at the end of each year for the next 40 years.

Required:

Calculate how much your accumulated investment is expected to be in 40 years.

Calculate the present value of an annuity(LO3)

EC–8Denzel needs a new car. At the dealership, he finds the car that he likes. The dealership gives him two payment options:

1.Pay $55,000 for the car today.

2.Pay $4,000 at the end of each quarter for four years.

Required:

Assuming Denzel uses a discount rate of 12% (or 3% quarterly), determine which option gives him the lower cost.