Exam 5: The Time Value of Money

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You're ready to make the last of four equal, annual payments on a $1,000 loan with a 10% interest rate.If the amount of the payment is $315.47, how much of that payment is accrued interest?

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The present value of an annuity stream of $100 per year is $614 when valued at a 10% rate.By approximately how much would the value change if these were annuities due?

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Your real estate agent mentions that homes in your price range require a payment of $1,200 per month for 30 years at 9% interest compounded monthly.What is the size of the mortgage with these terms?

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For a given amount, the lower the discount rate, the less the present value.

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A perpetuity is a special form of an annuity.

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Lester's just signed a contract that will provide the firm with annual cash inflows of $28,000, $35,000, and $42,000 over the next three years with the first payment of $28,000 occurring one year from today.What is this contract worth today at a discount rate of 7.25%?

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Assume your uncle recorded his salary history during a 40-year career and found that it had increased 10-fold.If inflation averaged 4% annually during the period, then over his career his purchasing power:

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The APR on a loan must be equal to the effective annual rate when:

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How many monthly payments remain to be paid on an 8% compounded monthly mortgage with a 30-year amortization and monthly payments of $733.76, when the balance reaches one-half of the $100,000 mortgage?

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How much must be deposited today in an account earning 6% annually to accumulate a 20% down payment to use in purchasing a car one year from now, assuming that the car's current price is $20,000, and inflation will be 4%?

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Real interest rates:

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How much must be invested today in order to generate a 5-year annuity of $1,000 per year, with the first payment 1 year from today, at an interest rate of 12%?

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The Excel function for present value is PV (rate, per, pmt, FV).

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As long as the interest rate is positive, the future value will always be larger than the present value given any period of time.

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To calculate present value, we discount the future value by some interest rate r, the discount rate.

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Approximately how much should be accumulated by the beginning of retirement to provide a $2,500 monthly check that will last for 25 years, during which time the fund will earn 6% interest with monthly compounding?

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A furniture store is offering free credit on purchases over $1,000.You observe that a big-screen television can be purchased for nothing down and $4,000 due in one year.The store next door offers an identical television for $3,650 but does not offer credit terms.Which statement below best describes the cost of the "free" credit?

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What is the present value of your trust fund if you have projected that it will provide you with $50,000 on your 30th birthday (7 years from today) and it earns 10% compounded annually?

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What will be the monthly payment on a home mortgage of $75,000 at 12% interest compounded monthly, to be amortized over 30 years?

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Would a depositor prefer an APR of 8% with monthly compounding or an APR of 8.5% with semiannual compounding?

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