Question 1

-You are borrowing $17,800 to buy a car.The terms of the loan call for monthly payments for 5 years at 8.6 percent interest.What is the amount of each payment?

Accepted Answer

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-You are borrowing $17,800 to buy...

Question 2

-The Design Team just decided to save $1,500 a month for the next 5 years as a safety net for recessionary periods.The money will be set aside in a separate savings account which pays 4.5 percent interest compounded monthly.The first deposit will be made today.What would today's deposit amount have to be if the firm opted for one lump sum deposit today that would yield the same amount of savings as the monthly deposits after 5 years?

Accepted Answer

Using the formula for future value of an annuity with monthly payments:

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

Where FV is the future value, PMT is the monthly payment, r is the annual interest rate (4.5%), n is the number of compounding periods per year (12), and t is the number of years (5).

Plugging in the numbers:

FV = $1,500 * [(1 + 0.045/12)^(12*5) - 1] / (0.045/12)
FV = $98,274.81

To find the lump sum deposit that would yield the same amount of savings after 5 years, we can use the formula for future value of a lump sum:

FV = PV * (1 + r/n)^(n*t)

Where PV is the present value (the lump sum deposit), all other variables are the same as before.

Plugging in the numbers and solving for PV:

$98,274.81 = PV * (1 + 0.045/12)^(12*5)
PV = $80,760.79

Therefore, the lump sum deposit that would yield the same amount of savings after 5 years is $80,760.79. Choice B is the correct answer.

Question 3

-Theresa adds $1,500 to her savings account on the first day of each year.Marcus adds $1,500 to his savings account on the last day of each year.They both earn 6.5 percent annual interest.What is the difference in their savings account balances at the end of 35 years?

Accepted Answer

Difference = $198,145.42 - $186,052.04 = $12,093Note: Difference = $186,052.04 × 0.065 = $12,093

Question 4

You need $25,000 today and have decided to take out a loan at 7 percent for five years.Which one of the following loans would be the least expensive? Assume all loans require monthly payments and that interest is compounded on a monthly basis.

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Question 5

-What is the future value of $1,200 a year for 40 years at 8 percent interest? Assume annual compounding.

Accepted Answer

This is a case of annuity, where a fixed amount is invested every year. The formula for the future value of an annuity is FV = PMT x (((1 + r)^n - 1) / r), where PMT is the annual payment, r is the annual interest rate, and n is the number of years. Plugging in the values, we get FV = 1200 x (((1 + 0.08)^40 - 1) / 0.08) = $310,868. Therefore, the best choice is C.

Question 6

-Trish receives $450 on the first of each month.Josh receives $450 on the last day of each month.Both Trish and Josh will receive payments for next four years.At a 9.5 percent discount rate,what is the difference in the present value of these two sets of payments?

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-Trish receives $450 on the first of...

Question 7

-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 $30 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 2 percent interest per month.How much money are you borrowing?

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-You need some money today and the...

Question 8

-Phil can afford $200 a month for 5 years for a car loan.If the interest rate is 7.5 percent,how much can he afford to borrow to purchase a car?

Accepted Answer

Using the formula for calculating loan payments:
P = (r * A) / (1 - (1 + r)^(-n))
where P is the loan principal, A is the monthly payment, r is the interest rate, and n is the number of months.

We know A = $200, r = 0.075/12 (monthly interest rate), and n = 5 years * 12 months/year = 60 months.

Solving for P gives:
P = (0.00625 * 200) / (1 - (1 + 0.00625)^(-60))
P = $9,981.06

Therefore, Phil can afford to borrow $9,981.06 to purchase a car. Option C is the closest to this amount.

Question 9

-You just won the grand prize in a national writing contest! As your prize,you will receive $2,000 a month for ten years.If you can earn 7 percent on your money,what is this prize worth to you today?

Accepted Answer

This problem involves finding the present value of a future stream of payments. We can use the formula for the present value of an annuity to solve it: PV = PMT * [(1 - (1 + r)^-n) / r], where PV is the present value, PMT is the payment amount, r is the interest rate, and n is the number of periods. Plugging in the values given, we get PV = $2,000 * [(1 - (1 + 0.07)^-120) / 0.07] = $172,252.71. Therefore, the best choice is A.

Question 10

-What is the future value of $12,000 a year for 25 years at 12 percent interest?

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Question 11

-Your employer contributes $50 a week to your retirement plan.Assume that you work for your employer for another 20 years and that the applicable discount rate is 9 percent.Given these assumptions,what is this employee benefit worth to you today?

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-Your employer contributes $50 a week to...

Question 12

-You are comparing two annuities with equal present values.The applicable discount rate is 8.75 percent.One annuity pays $5,000 on the first day of each year for 20 years.How much does the second annuity pay each year for 20 years if it pays at the end of each year?

Accepted Answer

Because each payment is received one year later, then the cash flow has to equal:$5,000 × (1 + 0.0875) = $5,438

Question 13

-You are the beneficiary of a life insurance policy.The insurance company informs you that you have two options for receiving the insurance proceeds.You can receive a lump sum of $200,000 today or receive payments of $1,400 a month for 20 years.You can earn 6 percent on your money.Which option should you take and why?

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Question 14

-You are scheduled to receive annual payments of $5,100 for each of the next 7 years.The discount rate is 10 percent.What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year?

Accepted Answer

Difference = $27,312 - $24,829 = $2,483Note: The difference = 0.1 × $24,829 = $2,483

Question 15

-Nadine is retiring at age 62 and expects to live to age 85.On the day she retires,she has $402,000 in her retirement savings account.She is somewhat conservative with her money and expects to earn 6 percent during her retirement years.How much can she withdraw from her retirement savings each month if she plans to spend her last penny on the morning of her death?

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-Nadine is retiring at age 62 and...

Question 16

-Holiday Tours (HT)has an employment contract with its newly hired CEO.The contract requires a lump sum payment of $10.4 million be paid to the CEO upon the successful completion of her first three years of service.HT wants to set aside an equal amount of money at the end of each year to cover this anticipated cash outflow and will earn 5.65 percent on the funds.How much must HT set aside each year for this purpose?

Accepted Answer

To find the amount HT must set aside each year, we use the formula for the future value of an annuity. The future value (FV) is $10.4 million, the interest rate (i) is 5.65%, and the number of periods (n) is 3 years. Rearranging the future value of an annuity formula to solve for the annuity payment (PMT) gives us:$$PMT = \frac{FV}{\left[\frac{(1 + i)^n - 1}{i}\right]}$$Plugging in the values:$$PMT = \frac{10,400,000}{\left[\frac{(1 + 0.0565)^3 - 1}{0.0565}\right]}$$$$PMT = \frac{10,400,000}{\left[\frac{(1.0565)^3 - 1}{0.0565}\right]}$$$$PMT = \frac{10,400,000}{3.184467}$$$$PMT ≈ 3,277,973$$Therefore, HT must set aside approximately $3,277,973 each year.

Question 17

-Alexa plans on saving $3,000 a year and expects to earn an annual rate of 10.25 percent.How much will she have in her account at the end of 45 years?

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Question 18

Your grandmother is gifting you $125 a month for four years while you attend college to earn your bachelor's degree.At a 6.5 percent discount rate,what are these payments worth to you on the day you enter college?

Accepted Answer

We need to find the present value of an annuity. Using the formula:

PV = Payment x [1 - (1 + r/12)^(-n*12)] / (r/12)

Where PV is the present value, Payment is the monthly payment, r is the discount rate, and n is the number of years.

Plugging in the given values:

PV = 125 x [1 - (1 + 0.065/12)^(-4*12)] / (0.065/12) = $5,270.94

Therefore, the answer is B, $5,270.94.

Question 19

-You borrow $165,000 to buy a house.The mortgage rate is 4.5 percent and the loan period is 30 years.Payments are made monthly.If you pay the mortgage according to the loan agreement,how much total interest will you pay?

Accepted Answer

To calculate the total interest paid, we need to use the formula for amortization, which is:

Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate) ^ (-Loan Period in Months))

Plugging in the values, we get:

Payment = (165,000 * 0.00375) / (1 - (1 + 0.00375) ^ (-30*12))
Payment = $839.22

To find the total interest paid, we need to subtract the original loan amount from the total amount paid over the loan period:

Total Interest = (Payment * Loan Period in Months) - Loan Amount
Total Interest = ($839.22 * 30*12) - $165,000
Total Interest = $135,971

Therefore, the correct answer is C.

Question 20

-You buy an annuity that will pay you $24,000 a year for 25 years.The payments are paid on the first day of each year.What is the value of this annuity today if the discount rate is 8.5 percent?

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-You buy an annuity that will...

Quiz 6: Discounted Cash Flow Valuation