Question 1

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?

Accepted Answer

The answer of You need some money today and the...

Question 2

An amortized loan:

Accepted Answer

An amortized loan may have equal or increasing amounts applied to the principal from each loan payment. This means that the loan payments are structured so that a portion of each payment goes towards paying down the principal balance, in addition to paying interest. Over time, as more principal is paid down, the amount of interest owed decreases, so a greater portion of each payment can go towards paying down the principal.

Question 3

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 prize's present value can be calculated using the formula for the present value of an annuity: PV = PMT × [(1 - (1 + r)^-n) / r], where PMT is the monthly payment ($2,000), r is the monthly interest rate (7% annually, so 0.07/12 monthly), and n is the total number of payments (10 years × 12 months = 120 payments). Plugging these values into the formula gives a present value of approximately $172,252.71.

Question 4

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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The answer of You are the beneficiary of a life...

Question 5

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?

Accepted Answer

The answer of Trish receives $450 on the first of...

Question 6

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

To find the present value of an annuity, we can use the formula PV = PMT x [(1 - (1 / (1 + r)^n)) / r], where PV is the present value, PMT is the periodic payment, r is the discount rate, and n is the number of periods.

In this case, PMT = $125, r = 6.5%, and n = 48 (4 years x 12 months/year). Plugging these values into the formula, we get:

PV = $125 x [(1 - (1 / (1 + 0.065)^48)) / 0.065]
PV = $5,270.94

Therefore, choice B is the correct answer.

Question 7

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 8

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

The monthly deposit amount can be calculated using the formula:

Future Value = Present Value * (1 + (interest rate/number of compounding periods))^(number of compounding periods * time)

where the present value is the monthly deposit amount, interest rate is 4.5%, number of compounding periods is 12 (monthly), and time is 5 years.

Future Value = $1,500 * (1 + (0.045/12))^(12*5)
Future Value = $98,406.46

To find the lump sum deposit that would yield the same future value, we can use the formula:

Present Value = Future Value / (1 + (interest rate/number of compounding periods))^(number of compounding periods * time)

where the future value is $98,406.46, interest rate is 4.5%, number of compounding periods is 12 (monthly), and time is 5 years.

Present Value = $98,406.46 / (1 + (0.045/12))^(12*5)
Present Value = $80,760.79

Therefore, the lump sum deposit that would yield the same savings as the monthly deposits after 5 years is $80,760.79.

Question 9

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

Accepted Answer

Using the formula for Future Value of an Annuity:
FV = Pmt x [((1 + r)^n - 1) / r]
where:
Pmt = $1,200
r = 8% = 0.08
n = 40

FV = $1,200 x [((1 + 0.08)^40 - 1) / 0.08]
FV = $310,868.

Question 10

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 11

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?

Accepted Answer

The answer of Alexa plans on saving $3,000 a year...

Question 12

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

Accepted Answer

The answer of What is the future value of $12,000...

Question 13

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?

Accepted Answer

The answer of You buy an annuity that will pay...

Question 14

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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The answer of Your employer contributes $50 a week to...

Question 15

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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The answer of You need $25,000 today and have decided...

Question 16

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

The answer of You are borrowing $17,800 to buy a...

Question 17

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 18

How is the principal amount of an interest-only loan repaid?

Accepted Answer

In an interest-only loan, the borrower only pays interest during the loan period and the principal amount is typically repaid in a lump sum at the end of the loan period. This is known as a balloon payment.

Question 19

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 20

The entire repayment of which one of the following loans is computed simply by computing a single future value?

Accepted Answer

A pure discount loan involves borrowing a lump sum of money and repaying it with a single future value, making it the only loan where the entire repayment is computed simply by computing a single future value.

Quiz 6: Discounted Cash Flow Valuation