Question 1

An insurance company offers you an end-of-year annuity of $48,000 per year for the next 20 years. They claim your return on the annuity is 9 percent. What should you be willing to pay today for this annuity?

Accepted Answer

We can use the annuity formula to calculate the present value of the annuity.
PV = C[(1 - (1 / (1 + r)^n)) / r]
where PV is the present value, C is the annual payment, r is the interest rate per period, and n is the number of periods.
Plugging in the given values, we get:
PV = 48,000[(1 - (1 / (1 + 0.09)^20)) / 0.09] = $438,192
Therefore, you should be willing to pay $438,192 today for this annuity.

Question 2

Your firm, New Sunrise, has just leased a $28,000 BMW for you. The lease requires six beginning-of-the-year payments that will fully amortize the cost of the car. What is the amount of the payments if the interest rate is 12 percent?

Accepted Answer

The answer of Your firm, New Sunrise, has just leased...

Question 3

Idlewild Bank has granted you a seven-year loan for $50,000. If your seven annual end-of-the-year payments are $11,660.45, what is the rate of interest Idlewild is charging?

Accepted Answer

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Question 4

BB&C bank has agreed to lend you $30,000 today, but you must repay $42,135 in 3 years. What rate is the bank charging you?

Accepted Answer

We can use the formula for compound interest to solve for the interest rate:

Future value = Present value x (1 + interest rate)^n

where:
Present value = $30,000
Future value = $42,135
n = 3 years

42,135 = 30,000 x (1 + interest rate)^3
1 + interest rate = (42,135/30,000)^(1/3)
1 + interest rate = 1.12
interest rate = 0.12 or 12%

Therefore, the bank is charging a rate of 12%. Option (C) is the correct answer.

Question 5

In six years, your daughter will be going to college. You wish to have a fund that will provide her $10,000 per year (end of year) for each of her four years in college. How much must you put into that fund today if the fund will earn 10 percent in each of the 10 years?

Accepted Answer

The present value of the annuity needed for the four years of college is calculated using the formula for the present value of an annuity. Then, this amount is discounted back six years to find the amount needed today.

Question 6

The lease on a new office requires an immediate payment of $24,000 plus $24,000 per year at the end of each of the next 10 years. At a discount rate of 14 percent, what is the present value of this stream of lease payments?

Accepted Answer

The present value of the lease payments can be calculated using the formula for the present value of an annuity plus the present value of the immediate payment. The immediate payment of $24,000 is already in present value terms, so it doesn't need to be discounted. The annuity formula is PV = P * [(1 - (1 + r)^-n) / r], where P is the payment ($24,000), r is the discount rate (14% or 0.14), and n is the number of periods (10 years). The present value of the annuity (the $24,000 per year for 10 years) is:PV = $24,000 * [(1 - (1 + 0.14)^-10) / 0.14] ≈ $125,194Adding the immediate payment of $24,000 gives a total present value of:$125,194 + $24,000 = $149,194

Question 7

You have just won a $50,000 bond that pays no interest and matures in 20 years. If the discount rate is 10%, what is the present value of your bond?

Accepted Answer

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Question 8

Columbia Bank & Trust has just given you a $20,000 term loan to pay for a new concrete mixer. The loan requires five equal annual end-of-the-year payments. If the loan provides the bank with a 12 percent return, what will be your annual payments?

Accepted Answer

Using the present value of an annuity formula:

PV of loan = A * [1 - (1+r)^(-n)] / r

Where A = annual payment, r = annual interest rate, n = number of years

Plugging in the values:

$20,000 = A * [1 - (1+0.12)^(-5)] / 0.12

$20,000 * 0.12 = A * [1 - (1.12)^(-5)]

$2,400 = A * 0.576

A = $5,547.85 (rounded to the nearest cent)

Therefore, the annual payments will be $5,547.85. Choice A is the correct answer.

Question 9

New Jersey Mutual has offered you a single premium annuity that will pay you $12,000 per year (end of year) for the next 15 years. If you must pay $109,296 today for this annuity, what is your expected rate of return?

Accepted Answer

The expected rate of return for an annuity can be calculated using the present value formula for annuities. In this case, the present value ($109,296) equals the annual payment ($12,000) divided by the rate of return. Using a financial calculator or an annuity present value formula, you can solve for the rate of return that makes the present value of the annuity payments equal to the cost of the annuity ($109,296). The correct rate of return that matches this scenario is approximately 7%.

Question 10

Joe Brady just won a $450,000 lottery in Pennsylvania. Instead of receiving a lump sum, he found that he would receive $22,500 annually (end of year) for 20 years. Joe is 75 years old and wants his money now. He has been offered $140,827 to sell his ticket. What rate of return is the buyer expecting to make if Joe accepts the offer?

Accepted Answer

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Question 11

Alabama Power has preferred stock that pays an annual dividend of $9.44. If the security has no maturity, what is its value to an investor who wishes to obtain a 9 percent rate of return?

Accepted Answer

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Question 12

Baggos has seen its EPS increase from $0.30 to $3.16 in seven years. What has been the growth rate of Baggos's EPS?

Accepted Answer

To calculate the growth rate of EPS, we use the formula:

Growth rate = [(Ending value/Beginning value)^(1/number of years)] - 1

Plugging in the given values:

Growth rate = [(3.16 / 0.30)^(1/7)] - 1
Growth rate = 1.398 -1
Growth rate = 0.398 or 39.8%

Rounding to the nearest 10%, the growth rate of Baggos's EPS is about 40%. Therefore, choice B is the best answer.

Question 13

John is 25 years old and wishes to retire in 30 years. His plan is to invest in a mutual fund earning a 12 percent annual return and have a $1 million retirement fund at age 55. How much must he invest at the end of each year to achieve this goal?

Accepted Answer

To solve this, we use the formula for the future value of an annuity: FV = P * [((1 + r)^n - 1) / r], where FV is the future value ($1,000,000), P is the annual payment, r is the annual interest rate (12% or 0.12), and n is the number of years (30). Rearranging the formula to solve for P gives P = FV / [((1 + r)^n - 1) / r]. Plugging in the values gives P = $1,000,000 / [((1 + 0.12)^30 - 1) / 0.12] ≈ $4,143.65.

Question 14

Designs Now is opening a showcase office to display and sell its computer-designed poster art. Designs expects cash flows to be $120,000 in the first year, $180,000 in the second year, $240,000 in the third year. If Designs uses 11 percent as its discount rate, what is the present value of the cash flows?

Accepted Answer

The correct answer is A because the present value of the cash flows is $429,720. This is calculated by using the formula for the present value of an annuity, which is:PV = CF * [1 - (1 + r)^-n] / rwhere:PV is the present valueCF is the cash flowr is the discount raten is the number of yearsIn this case, the cash flows are $120,000, $180,000, and $240,000, the discount rate is 11%, and the number of years is 3. Plugging these values into the formula, we get:PV = $120,000 * [1 - (1 + 0.11)^-3] / 0.11= $120,000 * [1 - 0.743] / 0.11= $120,000 * 0.257 / 0.11= $429,720

Question 15

What is the effective rate of interest on a CD that has a nominal rate of 9.5 percent with interest compounded monthly?

Accepted Answer

The effective rate of interest on a CD with a nominal rate of 9.5 percent compounded monthly can be calculated using the formula: 
Effective rate = (1 + (nominal rate/number of times interest is compounded))^number of times interest is compounded - 1 
Plugging in the values, we get: 
Effective rate = (1 + (0.095/12))^12 - 1 
Effective rate = 0.0993 or 9.93% 
Therefore, the answer is A.

Question 16

The Florida lottery agrees to pay the winner $250,000 at the end of each year for the next 20 years. What is the future value of this lottery if you plan to put each payment in an account earning 9 percent?

Accepted Answer

The future value of an annuity can be calculated using the formula FV = P * [((1 + r)^n - 1) / r], where P is the payment amount, r is the interest rate per period, and n is the number of periods. Plugging in the values ($250,000 for P, 9% or 0.09 for r, and 20 for n), the calculation gives a future value of approximately $12.79 million, making option B the correct answer.

Question 17

Jane wants to have $200,000 in an account in 20 years. If her account earns 11 percent per annum over the accumulation period, how much must she save per year (end of year) to have the $200,000?

Accepted Answer

This is a present value of an annuity problem. We need to find the annual payment that, when compounded annually at 11%, will result in a future value of $200,000 at the end of 20 years. Using the formula for present value of an annuity:

PMT = FV / (((1 + r)^n - 1) / r)

where PMT is the annual payment, FV is the future value, r is the interest rate per period (11% per year in this case), and n is the number of periods (20 years in this case). Plugging in the numbers, we get:

PMT = 200000 / (((1 + 0.11)^20 - 1) / 0.11) = $3,115.06

So Jane needs to save $3,115.06 per year (end of year) to have $200,000 in 20 years. The closest answer choice is B.

Question 18

Many IRA fund managers argue that investors should invest at the beginning of the year rather than at the end. What is the difference to an investor who invests $2,000 per year at 11 percent over a 30-year period?

Accepted Answer

Investing at the beginning of the year allows the investment to compound for an additional year each time, leading to a larger total amount due to the effect of compound interest.

Question 19

Billy Bob has decided to put $2,400 a year (at the end of each year) into an IRA over his 40-year working life and then retire. What will Billy have if the account will earn 10 percent compounded annually?

Accepted Answer

We can solve this using the formula for future value of an annuity: FV = C * [(1 + r)^n - 1]/r, where C is the annual contribution, r is the interest rate, and n is the number of years. Plugging in the numbers, we get: FV = 2,400 * [(1 + 0.1)^40 - 1]/0.1 = $1,062,223. Therefore, the correct answer is C.

Question 20

What is the future value of a $10,000 college tuition fund if the nominal rate of interest is 12 percent compounded monthly for five years?

Accepted Answer

The answer of What is the future value of a...

Quiz 5: The Time Value of Money