Exam 2: How to Calculate Present Values

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The concept of compound interest is most appropriately described as:

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An investment at 10% nominal rate compounded continuously is equal to an equivalent annual rate of:

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If the present value annuity factor at 10% APR for 10 years is 6.1446, what is the equivalent future value annuity factor?

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What is the present value of $10,000 per year perpetuity at an interest rate of 10%?

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The present value of a future cash flow can be found by dividing it by an appropriate discount factor.

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What is the present value of $5000 per year annuity at a discount rate of 10% for 6 years?

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Describe how you would go about finding the present value of any annuity given the formula for the present value of a perpetuity.

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Mr. Hopper is expected to retire in 30 years and he wishes accumulate $1,000,000 in his retirement fund by that time. If the interest rate is 12% per year, how much should Mr. Hopper put into the retirement fund each year in order to achieve this goal?

(Multiple Choice)
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If the present value of $1.00 received n years from today at an interest rate of r is 0.3855, then what is the future value of $1.00 invested today at an interest rate of r% for n years?

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The rate of return on any perpetuity is equal to the cash flow multiplied by the price.

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You would like to have enough money saved to receive a growing annuity for 25 years, growing At a rate of 4% per year, the first payment being $60,000 after retirement, so that you and your family can lead a good life. How much would you need to save in your retirement fund to achieve this goal? (assume that the growing perpetuity payments start one year from the date of Your retirement. The interest rate is 12%)?

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The discount rate is used for calculating the NPV is:

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You would like to have enough money saved to receive a growing annuity for 20 years, growing at a rate of 5% per year, the first payment being $50,000 after retirement. That way, you hope that you and your family can lead a good life after retirement. How much would you need to save in your retirement fund to achieve this goal.(assume that the growing annuity payments start one year from the date of your retirement. The interest rate is 10%)?

(Multiple Choice)
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Mr. Hopper is expected to retire in 25 years and he wishes accumulate $750,000 in his retirement fund by that time. If the interest rate is 10% per year, how much should Mr. Hopper put into the retirement fund each year in order to achieve this goal? [Assume that the payments are made at the end of each year]

(Multiple Choice)
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You would like to have enough money saved to receive an $80,000 per year perpetuity after retirement so that you and your family can lead a good life. How much would you need to save in your retirement fund to achieve this goal (assume that the perpetuity payments starts on the day of retirement. The interest rate is 10%)?

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Discuss why a dollar tomorrow cannot be worth less than a dollar the day after tomorrow.

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A perpetuity is defined as:

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The following statements regarding the NPV rule and the rate of return rule are true except:

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Mr. William expects to retire in 30 years and would like to accumulate $1 million in the pension fund. If the annual interest rate is 12% per year, how much should Mr. Williams put into the pension fund each month in order to achieve his goal? Assume that Mr. Williams will deposit the same amount each month into his pension fund and also use monthly compounding.

(Multiple Choice)
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The rate of return, discount rate, hurdle rate or opportunity cost of capital all means the same.

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