Question 1

You want to go to Europe 5 years from now, and you can save $3,100 per year, beginning 1 year from today. You plan to deposit the funds in a mutual fund that you expect to return 8.5% per year. Under these conditions, how much will you have just after you make the fifth deposit, 5 years from now?

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Question 2

You have a chance to buy an annuity that pays $550 at the BEGINNING of each year for 3 years. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

Accepted Answer

To find the price of the annuity, we need to calculate the present value of the future cash flows. Here's how to do it using the formula for the present value of an annuity:
PV = C * [(1 - (1 + r)^(-n)) / r]
where PV is the present value, C is the annual payment, r is the discount rate, and n is the number of years.

Plugging in the numbers from the problem, we get:
PV = 550 * [(1 - (1 + 0.055)^(-3)) / 0.055]
PV = $1,565.48

So the most you should pay for the annuity is $1,565.48. Choice C is the correct answer.

Question 3

You plan to invest in securities that pay 9.0%, compounded annually. If you invest $5,000 today, how many years will it take for your investment account to grow to $9,140.20?

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Question 4

What's the present value of a 4-year ordinary annuity of $2,250 per year plus an additional $3,000 at the end of Year 4 if the interest rate is 5%?

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Question 5

You own an oil well that will pay you $30,000 per year for 10 years, with the first payment being made today. If you think a fair return on the well is 8.5%, how much should you ask for if you decide to sell it?

Accepted Answer

We can use the Present Value formula to calculate the fair price for the well:
PV = CF / (1 + r)^n
where PV is the present value, CF is the cash flow, r is the interest rate, and n is the number of periods.

In this case, CF = $30,000 per year for 10 years, r = 8.5%, and n = 10. The first payment is already made, so we need to calculate the present value of the remaining 9 payments:
PV = $30,000 {(1 - (1 + 0.085)^-9) / 0.085} = $213,572

Therefore, the fair price to sell the well would be $213,572. The closest answer choice is B.

Question 6

Your uncle has $375,000 and wants to retire. He expects to live for another 25 years, and he also expects to earn 7.5% on his invested funds. How much could he withdraw at the BEGINNING of each of the next 25 years and end up with zero in the account?

Accepted Answer

To calculate this, we need to use the Present Value of an Annuity formula, which is:

Payment = (PV x r) / (1 - (1 + r)^(-n))

Where PV is the present value of the funds ($375,000), r is the interest rate (7.5%), and n is the number of payments (25).

Plug in the numbers:

Payment = (375,000 x 0.075) / (1 - (1 + 0.075)^(-25))
Payment = $31,294.42 (rounded to the nearest cent)

Therefore, the uncle could withdraw $31,294.42 at the beginning of each of the next 25 years and end up with zero in the account. Choice C is the closest answer.

Question 7

Your uncle has $375,000 and wants to retire. He expects to live for another 25 years, and to be able to earn 7.5% on his invested funds. How much could he withdraw at the end of each of the next 25 years and end up with zero in the account?

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Question 8

Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the end of each of the next 20 years?

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Question 9

Your aunt is about to retire, and she wants to buy an annuity that will supplement her income by $65,000 per year for 25 years, beginning a year from today. The going rate on such annuities is 6.25%. How much would it cost her to buy such an annuity today?

Accepted Answer

We can use the present value of an annuity formula: PV = PMT * ((1 - (1+r)^(-n))/r), where PV is the present value, PMT is the annual payment, r is the interest rate, and n is the number of years.

Plugging in the values, we get: PV = $65,000 * ((1 - (1+0.0625)^(-25))/0.0625) = $811,540.16.

Therefore, the answer is B, and it would cost her $811,540.16 to buy such an annuity today.

Question 10

Your aunt is about to retire, and she wants to buy an annuity that will provide her with $65,000 of income a year for 25 years, with the first payment coming IMMEDIATELY. The going rate on such annuities is 6.25%. How much would it cost her to buy the annuity today?

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Question 11

You want to buy a new sports car 3 years from now, and you plan to save $4,200 per year, beginning 1 year from today. You will deposit your savings in an account that pays 5.2% interest. How much will you have just after you make the third deposit, 3 years from now?

Accepted Answer

Using the formula for future value of an annuity:

FV = Pmt * [(1 + r)^n - 1] / r

where:
Pmt = annual deposit amount = $4,200
r = annual interest rate = 5.2%
n = number of deposits = 3

We can calculate the future value of the deposits:

FV = $4,200 * [(1 + 0.052)^3 - 1] / 0.052
FV = $13,266.56

Therefore, the amount just after the third deposit, 3 years from now, will be $13,266.56.

Question 12

What is the PV of an annuity due with 10 payments of $2,700 at an interest rate of 6.5%?

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Question 13

Last year Mason Corp's earnings per share were $2.50, and its growth rate during the prior 5 years was 9.0% per year. If that growth rate were maintained, how many years would it take for Mason's EPS to double?

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Question 14

You want to go to Europe 5 years from now, and you can save $3,100 per year, BEGINNING IMMEDIATELY. You plan to deposit the funds in a mutual fund that you expect to return 8.5% per year. Under these conditions, how much will you have just after you make the fifth deposit, 5 years from now?

Accepted Answer

To calculate the future value of the savings, we can use the formula for the future value of an annuity:

FV = Pmt x [ (1 + r)^n - 1 ] / r

where:
Pmt = annual savings amount
r = annual interest rate
n = number of years

Using this formula, we can calculate the future value of the savings just after the fifth deposit:

FV = $3,100 x [ (1 + 0.085)^5 - 1 ] / 0.085
   = $3,100 x 6.3529
   = $19,706.49

Therefore, the closest answer choice is C ($19,929.99).

Question 15

You want to buy a new sports car 3 years from now, and you plan to save $4,200 per year, BEGINNING IMMEDIATELY. You will make three deposits in an account that pays 5.2% interest. Under these assumptions, how much will you have 3 years from today?

Accepted Answer

The correct answer is A because the future value of the three deposits, each of $4,200, made at the end of each year for three years at 5.2% interest, is $13,956.42.

Question 16

You have a chance to buy an annuity that pays $1,200 at the end of each year for 3 years. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

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Question 17

What is the PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 6.5%?

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Question 18

Your uncle has $375,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $35,000 at the end of each year, beginning at the end of this year. How many years will it take to exhaust his funds, i.e., run the account down to zero?

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Question 19

Your uncle has $500,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $40,000 at the BEGINNING of each year, beginning immediately. How many years will it take to exhaust his funds, i.e., run the account down to zero?

Accepted Answer

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Question 20

Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the BEGINNING of each of the next 20 years?

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