Questions and Answers
What is the present value of a security that will pay $29,000 in 20 years at an annuity rate of 5%?
$10,929.80
If you deposit money today in an account that pays 4% annual interest, how long will it take to double your money?
17.67 years
What is the future value of a 5%, 5-year ordinary annuity that pays $800 each year?
$4,420.51
If the ordinary annuity payment was an annuity due, what would its future value be?
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What will be the monthly loan payment for a $40,000 loan amortized over 5 years at an 8% nominal interest rate?
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What is the effective annual rate (EAR) for the same loan?
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Find the future value of $500 per year for 8 years at an interest rate of 14%.
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What is the present value of a $600 perpetuity if the interest rate is 5%?
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Find the present values of the cash flow streams at a 5% discount rate.
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What is a common recommendation for a rookie quarterback negotiating a contract with an opportunity cost of 7%?
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What are the dollar amounts for the payments Jan receives for her $10,000 mortgage?
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Find the present value of $500 due in the future under a 12% nominal rate, discounted back over 5 years.
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How much can a down payment of $4,000 yield if monthly payments of $350 are made at a 12% APR over 48 and 60 months?
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Study Notes
Present Value and Future Value
- Present value of a security paying $29,000 in 20 years at 5% risk-adjusted rate is $10,929.80.
- Future value of an ordinary annuity of $800 for 5 years at 5% is $4,420.51; if it were an annuity due, the value would be $4,641.53.
- Present values are sensitive to interest rates; as rates increase, present values decrease.
Interest Rates and Loan Payments
- Time to double an investment at 4% interest is approximately 17.67 years.
- Monthly payment for a fully amortized $40,000 loan over 5 years at 8% interest is $811.06, with an effective annual rate (EAR) of 8.30%.
- To calculate interest on loans and investments, use the formula for effective rate based on the terms of repayment.
Compounding and Discounting
- Compounded values: $200 at 4% for 10 years results in $296.05; at 8%, it would grow to $432.64.
- Present value calculations require adjusting the future cash flow according to set interest rates, with a higher rate leading to lower present value.
Future Values of Annuities
- Future values of ordinary annuities vary based on compounding rates. For example:
- $500 annually for 8 years at 14% yields greater total than $250 annually for 4 years at 7%.
- Adjusting to annuities due increases these future values due to earlier cash flow timing.
Perpetuities and Cash Flow Streams
- Present value of a $600 perpetuity at 5% interest is $12,000; at 10%, it decreases to $6,000.
- Analyzing cash flow streams at 5% discounting reveals different present values for changing cash flow patterns.
Contract Negotiation
- Evaluate NFL contract offers based on present value; for instance, Contract 1 offers consistent payments, while Contract 2 presents increasing values over time.
- Recommend contracts based on maximizing present value given an opportunity cost of 7%.
Mortgage Payments and Interest Reporting
- A $10,000 mortgage at 10% nominal interest with semiannual payments will require calculations for payment amounts and interest/principal breakdown.
- Interest income will fluctuate over time even with constant payments due to amortization effects.
Present Value Evaluation
- For future cash flows, present values diminish rapidly over longer periods and higher compounding rates.
- Differences in present values arise from compounding frequency; more frequent compounding results in lower present values.
Car Financing Considerations
- Saving $4,000 with maximum monthly payments of $350 for car loans determines affordability based on interest (12% APR).
- Loan terms impact the maximum price of the car one can afford, with longer terms allowing for higher total financing.
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Description
Test your understanding of Chapter 5 in Finance 341 with these flashcards. The quiz covers essential concepts such as present value, future value, and annuities. Use this as a study guide to prepare for your exam efficiently.
