Question 1

A friend who owns a perpetuity that promises to pay $1,000 at the end of each year,forever,comes to you and offers to sell you all of the payments to be received after the 25th year for a price of $1,000.At an interest rate of 10 percent,should you pay the $1,000 today to receive payment numbers 26 and onwards?
 What does this suggest to you about the value of perpetual payments?

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Question 2

Using the example of a savings account,explain the difference between the effective annual rate and the annual percentage rate.

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Question 3

You just won the lottery.To supplement your income you will receive twenty payments of $300,000 to be paid at the end of each of the next twenty years.Using a discount rate of 6%,calculate the present value of the annuity.

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Question 4

There are three factors that affect the present value of an annuity.Explain what these three factors are and discuss how an increase in each will impact the present value of the annuity.

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Question 5

If you invest $100,000 today at 12% per year over the next 15 years,what is the most you can spend in equal amounts out of the fund each year over that time?

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Question 6

What is the present value of four annual payments of $5,000 at a discount rate of 12%?

Accepted Answer

The present value of an annuity formula is:

PV = Payment * [1 - (1+r)^(-n)] / r

where PV is the present value, Payment is the amount of each payment, r is the discount rate, and n is the number of periods.

Plugging in the numbers, we get:

PV = $5,000 * [1 - (1+0.12)^(-4)] / 0.12
PV = $5,000 * [1 - 0.6355] / 0.12
PV = $5,000 * 0.3645 / 0.12
PV = $15,187.50

Therefore, the best choice is B, as it is the closest to our calculated present value.

Question 7

You are to receive $1000 per year indefinitely.The market rate of interest for these types of payments is 10%.The price you would pay for this stream is:

Accepted Answer

The price of a perpetuity is calculated as the annual payment divided by the interest rate. Here, $1000 / 0.10 = $10,000.00.

Question 8

Your elderly great uncle left you an annuity that will pay $100 next year and grow at an annual rate of 4%.The payments are expected to go on indefinitely and the interest rate is 7%.What is the value of the growing perpetuity?

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Question 9

The great,great grandparents of one of your classmates sold their factory to the government 110 years ago for $125,000.If these proceeds had been invested at 6%,how much would this legacy be worth today? Assume annual compounding.

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Question 10

There are three factors that affect the future value of an annuity.Explain what these three factors are and discuss how an increase in each will impact the future value of the annuity.

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Question 11

Mr.Miser,who is 35 years old,has just inherited $11,000 and decides to use the windfall towards his retirement.He places the money in a bank that promises a return of 6% per year until his planned retirement in 30 years.If his funds earn 6% interest compounded annually,how much will he have at retirement?
 Repeat the analysis for both semi-annual and continuous compounding.

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Question 12

What is the different between an ordinary annuity and an annuity due?
 Which occurs more in practice?
 Give a common example of both.

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Question 13

Your aunt,in her will,left you the sum of $5,000 a year forever with payments starting immediately.However,the news is better.She has specified that the amount should grow at 5% per year to maintain purchasing power.Given an interest rate of 12%,what is the PV of the inheritance?

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Quiz 4: Discounted Cash Flow Valuation