Question

1. Solve the following financial problems using the time value of money functions in Excel (PV, FV, PMT, NPER, RATE, EFFECT) OR using your financial calculator.
   • Assume you deposit $3,000 today, and $300 at the end of each year, in an account earning 4% per year for 20 years. What is the future value?
   • General Electric has an unfunded pension liability of $300 million that must be paid in 15 years. The CFO deposits $10 million in account today to help meet this goal, and will also deposit $8 million at the end of the next 15 years, to meet this liability. What annual rate of interest must the account earn to meet the liability?
   • What is the present value of an ordinary annuity that promises $20,000 per year for 20 years if the appropriate discount rate is 5%?
   • What is the present value of an annuity due that promises $20,000 per year for 20 years if the appropriate discount rate is 5%?
   • What is the future value of an ordinary annuity that promises $60,000 per year for 10 years if the appropriate interest rate is 4%?
   • What is the future value of an annuity due that promises $60,000 per year for 10 years if the appropriate interest rate is 4%?
   • You recently received a credit card that quotes an annual percentage rate (APR) of 24%. The card requires monthly payments. What is the effective annual rate (EAR)?

Answer 1

• Assume you deposit $3,000 today, and $300 at the end of each year, in an account earning 4% per year for 20 years. What is the future value?

N = 20, I/Y = 4, PV = -3,000, PMT = -300

CPT FV

FV = $15,506.793

• General Electric has an unfunded pension liability of $300 million that must be paid in 15 years. The CFO deposits $10 million in account today to help meet this goal, and will also deposit $8 million at the end of the next 15 years, to meet this liability. What annual rate of interest must the account earn to meet the liability?

FV = 300,000,000

N = 15

PV = -10,000,000

PMT = -8,000,000

CPT I/Y

I/Y = 10.15542204

The annual rate of interest that the account must earn to meet the liability is 10.15542204%

• What is the present value of an ordinary annuity that promises $20,000 per year for 20 years if the appropriate discount rate is 5%?

N = 20

I/Y = 5

FV = 0

PMT = 20,000

CPT PV

PV = -249,244.2069

The present value of the ordinary annuity = $249,244.2069

• What is the present value of an annuity due that promises $20,000 per year for 20 years if the appropriate discount rate is 5%?

Annuity due means the first payment is today. So, set the calculator to beginning mode.

N = 20

I/Y = 5

FV = 0

PMT = 20,000

CPT PV

PV = -261,706.4172

The present value of the annuity due = $261,706.4172

• What is the future value of an ordinary annuity that promises $60,000 per year for 10 years if the appropriate interest rate is 4%?

N = 10, I/Y = 4, PMT = 60,000, PV = 0

CPT FV

FV = -720,366.4274

The future value of the ordinary annuity = $720,366.4274

• What is the future value of an annuity due that promises $60,000 per year for 10 years if the appropriate interest rate is 4%?

Set the calculator to BGN mode

N = 10, I/Y = 4, PMT = 60,000, PV = 0

CPT FV

FV = -749,181.0845

The future value of the annuity due = $749,181.0845​​​​​​​

• You recently received a credit card that quotes an annual percentage rate (APR) of 24%. The card requires monthly payments. What is the effective annual rate (EAR)?

EAR = (1 + APR/12)^12 - 1

EAR = (1 + 0.24/12)^12 - 1

EAR = 0.2682417946

EAR = 26.82417946%

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