Question 1

Scott has been offered an employment contract for ten years at a starting salary of $65,000 with guaranteed annual raises of 5 percent.What is the current value of this offer at a discount rate of 7 percent?

Accepted Answer

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Question 2

Assume you could invest $25,000 at a continuously compounded rate of 10 percent.What would your investment be worth at the end of 50 years?

Accepted Answer

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Question 3

Anna's grandmother established a trust and deposited $250,000 into it.The trust pays a guaranteed 4.25 percent rate of return.Anna will receive all the interest earnings on an annual basis and a charity will receive the principal amount at Anna's passing.How much income will Anna receive each year?

Accepted Answer

To calculate the amount of income Anna will receive each year, we need to multiply the principal amount by the rate of return:
$250,000 x 4.25% = $10,625
Therefore, Anna will receive $10,625 in interest earnings each year. The correct answer is D.

Question 4

What is the future value of investing $5,650 for 14 years at a continuously compounded rate of 8.6 percent?

Accepted Answer

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Question 5

Uptown Industries just decided to save $3,000 a quarter for the next three years.The money will earn 2.75 percent,compounded quarterly,and the first deposit will be made today.If the company had wanted to deposit one lump sum today,rather than make quarterly deposits,how much would it have had to deposit to have the same amount saved at the end of the three years?

Accepted Answer

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Question 6

The preferred stock of ABC Co.offers a rate of return of 7.87 percent.The stock is currently priced at $63.53 per share.What is the amount of the annual dividend?

Accepted Answer

The annual dividend is calculated by multiplying the rate of return by the current price per share. So, $63.53 * 7.87% = $5.00.

Question 7

Lucas invested $4,500 at 6.2 percent,compounded continuously.What will his investment be worth after 15 years?

Accepted Answer

The formula for continuous compounding is A = Pe^(rt), where P is the principal, r is the rate, and t is the time. Plugging in the values: A = 4500 * e^(0.062*15) = 4500 * e^(0.93) ≈ 11,405.29.

Question 8

You want to establish a trust fund that will provide $50,000 a year forever for your heirs.If the fund can earn a guaranteed rate of return of 4.5 percent,how much must you deposit in a solitary lump sum to establish this trust?

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Question 9

Lois is purchasing an annuity that will pay $5,000 annually for 20 years,with the first annuity payment made on the date of purchase.What is the value of the annuity on the purchase date given a discount rate of 7 percent?

Accepted Answer

The annuity is an annuity due, meaning the first payment is made immediately. The present value of an annuity due can be calculated using the formula for the present value of an ordinary annuity and then multiplying by (1 + r) to account for the immediate payment. Using the formula for the present value of an ordinary annuity and adjusting for the annuity due, the value is approximately $56,677.98.

Question 10

Assume your employer will contribute $50 a week for twenty years to your retirement plan.At a discount rate of 5 percent,compounded weekly,what is this employee benefit worth to you today?

Accepted Answer

To find the present value of the weekly contributions, use the formula for the present value of an annuity: PV = Pmt * [(1 - (1 + r)^-n) / r], where Pmt is the weekly payment ($50), r is the weekly discount rate (0.05/52), and n is the total number of payments (20*52). Calculating this gives approximately $32,861.08.

Question 11

You are comparing two annuities with equal present values.The applicable discount rate is 6.5 percent.One annuity will pay $2,000 annually,starting today,for 20 years.The second annuity will pay annually,starting one year from today,for 20 years.What is the annual payment for the second annuity?

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Question 12

Denise will receive annual payments of $10,000 for the next 25 years.The discount rate is 6.8 percent.What is the difference in the present value of these payments if they are paid at the beginning of each year rather than at the end of each year?

Accepted Answer

The present value of an annuity due is greater than the present value of an ordinary annuity because the payments are made at the beginning of each period rather than at the end. The difference in the present value of these payments is $8,069.29.

Question 13

Wilt has a consulting contract that calls for annual payments of $50,000 a year for five years with the first payment due today.What is the current value of this contract if the discount rate is 8.4 percent?

Accepted Answer

The current value of the contract is calculated using the present value of an annuity due formula, as the first payment is made today. The formula for the present value of an annuity due is PV = Pmt * [(1 - (1 + r)^-n) / r] * (1 + r), where Pmt is the payment amount, r is the discount rate, and n is the number of periods. Using these values, the present value is $214,142.50.

Question 14

You need some money today and the only friend you have that has any is your 'miserly' friend.He agrees to loan you the money you need,if you make payments of $20 a month for the next six months.In keeping with his reputation,he requires that the first payment be paid today.He also charges you 1.5 percent interest per month.How much total interest does he expect to earn?

Accepted Answer

The total amount being loaned is not given, so let's assume it's $100 for simplicity. 
After the first payment of $20, the remaining balance is $80.
The interest on $80 at 1.5% per month is $1.20.
So for each subsequent month, $20 is paid towards the balance and an additional $1.20 is paid towards interest. 
The total interest earned over the 6-month period would be $1.20 x 6 = $7.20
However, at the end of the 6 months, the remaining balance would be very small and unlikely to accrue an additional $0.15 in interest. 
Therefore, the most reasonable answer choice is B) $4.35, which is the interest earned after the first payment and for the subsequent five months.

Question 15

A trust has been established to fund scholarships in perpetuity.The next annual distribution will be $1,200 and future payments will increase by 3 percent per year.What is the value of this trust at a discount rate of 7.4 percent?

Accepted Answer

This is a growing perpetuity problem, which can be solved using the formula: PV = D / (r - g), where PV is the present value of the trust, D is the next annual distribution ($1,200), r is the discount rate (7.4% or 0.074), and g is the growth rate (3% or 0.03). Plugging in the values: PV = $1,200 / (0.074 - 0.03) = $1,200 / 0.044 = $27,272.73.

Question 16

You just paid $525,000 for a security that will pay you and your heirs $25,000 a year forever.What rate of return will you earn?

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Question 17

Tracie will receive payments of $550 a month for ten years.What are these payments worth today at a discount rate of 6 percent,compounded monthly?

Accepted Answer

The present value of an annuity formula is used to calculate the current value of future payments at a given discount rate. The formula is PV = P * [(1 - (1 + r)^-n) / r], where PV is the present value, P is the payment amount, r is the monthly interest rate (annual rate divided by 12), and n is the total number of payments (months). Here, P = $550, r = 6%/12 = 0.005, and n = 10*12 = 120. Plugging these values into the formula gives PV = $550 * [(1 - (1 + 0.005)^-120) / 0.005], which calculates to approximately $49,540.40.

Question 18

Olivia is willing to pay $185 a month for four years for a car payment.If the interest rate is 4.9 percent,compounded monthly,and she has a cash down payment of $2,500,what price car can she afford to purchase?

Accepted Answer

To find the price of the car Olivia can afford, we need to calculate the present value of the annuity (monthly payments) and add the down payment. The formula for the present value of an annuity is:  PV = PMT × [(1 - (1 + r)^-n) / r]  Where PMT is the monthly payment ($185), r is the monthly interest rate (4.9% annual rate / 12 months = 0.0040833), and n is the total number of payments (4 years × 12 months = 48).  PV = 185 × [(1 - (1 + 0.0040833)^-48) / 0.0040833]  PV ≈ $8,049.07  Adding the down payment of $2,500 gives a total car price of $10,549.07.

Question 19

Benson's established a trust fund that provides $125,000 in college scholarships each year.The trust fund earns 6.15 percent and distributes only its annual income.How much money did Benson's contribute to establish this fund?

Accepted Answer

To find the principal amount that earns $125,000 annually at a 6.15% interest rate, use the formula: Principal = Annual Income / Interest Rate. Thus, Principal = $125,000 / 0.0615 = $2,032,520.

Question 20

A preferred stock pays an annual dividend of $6.50 a share and has an annual rate of return of 7.35 percent.What is the stock price?

Accepted Answer

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Quiz 4: Discounted Cash Flow Valuation