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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%?
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?
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?
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?
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?
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?
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%.
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%?
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.
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%?
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?
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.
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?
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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.
