Question 1

Stevenson Interiors of Kingston has a $67,500 liability they must pay four years from today. The company is opening a savings account so that the entire amount will be available when this debt needs to be paid. The plan is to make an initial deposit today and then deposit an additional $10,000 a year for the next four years, starting one year from today. The account pays a 5% rate of return. How much does the firm need to deposit today?

Accepted Answer

To find the initial deposit required today, we can use the future value of an annuity formula for the annual deposits and the future value formula for the single deposit today. The future value of the $67,500 liability needs to equal the future value of the initial deposit plus the future value of the annuity of $10,000 deposits. The formula for the future value of an annuity is $FV_{annuity} = P \times \frac{(1 + r)^n - 1}{r}$, where $P$ is the payment, $r$ is the interest rate per period, and $n$ is the number of periods. The future value of a single sum is $FV = PV \times (1 + r)^n$, where $PV$ is the present value or the initial deposit we're solving for. Rearranging the future value formula to solve for $PV$ gives us $PV = \frac{FV}{(1 + r)^n}$. Given that the future value needed is $67,500, the interest rate $r$ is 5% or 0.05, and the number of periods $n$ is 4 years, we can calculate the present value of the $10,000 annual deposits and then solve for the initial deposit required today to meet the future liability. The correct answer accounts for both the future value of the annuity and the present value calculation to meet the $67,500 future liability, which is option B, $20,072.91. This option correctly reflects the initial deposit needed today when considering the 5% rate of return over four years and the annual $10,000 deposits.

Question 2

Daryl wishes to save money to provide for his retirement. Beginning one month from now, he will begin depositing a fixed amount into a retirement savings account that will earn 12% compounded monthly. He will make 360 such deposits. Then, one year after making his final deposit, he will withdraw $100,000 annually for 25 years. The fund will continue to earn 12% compounded monthly. How much should the monthly deposits be for his retirement plan?

Accepted Answer

To find the monthly deposit, we need to calculate the future value of an annuity (the deposits) and set it equal to the present value of the withdrawals. The future value of the annuity formula is used for the deposits, and the present value of an annuity formula is used for the withdrawals. Solving these equations with the given interest rate and time periods, the monthly deposit comes out to approximately $214.21.

Question 3

Today is January 1. Starting today, Sam is going to contribute $140 on the first of each month to his retirement account. His employer contributes an additional 50% of the amount contributed by Sam. If both Sam and his employer continue to do this and Sam can earn a monthly rate of 0.5%, how much will he have in his retirement account 35 years from now?

Accepted Answer

This problem can be solved using the future value of a series formula in finance, which is used to calculate the future value of a series of cash flows at a given rate of return. Here, Sam contributes $140, and his employer contributes an additional 50% of that amount, which is $70, making the total monthly contribution $210.The formula for the future value of a series is:$$ FV = P \times \frac{(1 + r)^n - 1}{r} $$where:- $FV$ is the future value of the series,- $P$ is the payment amount per period,- $r$ is the interest rate per period,- $n$ is the total number of payments.Given:- $P = $210$ (Sam's contribution plus his employer's contribution),- $r = 0.5\% = 0.005$ (monthly interest rate),- $n = 35 \times 12 = 420$ months (since there are 35 years and 12 months in a year).Plugging these values into the formula gives:$$ FV = 210 \times \frac{(1 + 0.005)^{420} - 1}{0.005} $$$$ FV \approx $300,685.11 $$Therefore, the amount Sam will have in his retirement account 35 years from now is approximately $300,685.11.

Question 4

Janet plans on saving $3,000 a year and expects to earn 8.5%. How much will Janet have at the end of twenty-five years if she earns what she expects?

Accepted Answer

This problem can be solved by using the formula for future value of an annuity, which is FV = PMT x (((1 + r)^n - 1) / r), where PMT is the annual savings, r is the interest rate, and n is the number of years. Plugging in the given values, we get FV = $3,000 x (((1 + 0.085)^25 - 1) / 0.085) = $236,003.38, which is closest to choice C.

Question 5

You have a sub-contracting job with a local manufacturing firm. Your agreement calls for annual payments of $82,000 for the next 3 years. At a discount rate of 9.5%, what is this job worth to you today?

Accepted Answer

The answer of You have a sub-contracting job with a...

Question 6

You have a 25-year $400,000 mortgage with a 3.5% rate of interest (compounded monthly) that you make monthly payments on. What is the balance of the loan at the end of year 15?

Accepted Answer

To find the balance of the loan at the end of year 15, calculate the monthly payment using the loan formula, then determine the remaining balance after 180 payments (15 years). The correct balance is approximately $202,506.

Question 7

What would your payment be on a 10-year, $150,000 loan at 10% interest compounded semi-annually assuming the payments are made annually?

Accepted Answer

The answer of What would your payment be on a...

Question 8

You just borrowed $17,500 from the bank to use in your business. The loan terms require you to pay the interest annually with the entire principal due in four years. The interest rate is 9.5%. How much will you pay to the bank in year four of the loan?

Accepted Answer

The answer of You just borrowed $17,500 from the bank...

Question 9

Your parents are giving you $500 a month for five years while you attend college to earn both a bachelor's and a master's degree. At a 7% discount rate, what are these payments worth to you when you first enter college?

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The answer of Your parents are giving you $500 a...

Question 10

You are buying a previously owned car today at a price of $6,890. You are paying $500 down in cash and financing the balance for 36 months at 7.9%. What is the amount of each loan payment?

Accepted Answer

First, we need to find the total amount being financed.

Total amount = Price of car - Down payment
Total amount = $6,890 - $500
Total amount = $6,390

Next, we can use the formula for a loan payment:

Payment = (P * r) / (1 - (1 + r)^(-n))

Where P is the principal (total amount), r is the monthly interest rate (7.9% divided by 12), and n is the number of payments (36).

Payment = ($6,390 * 0.0079) / (1 - (1 + 0.0079)^(-36))
Payment = $49.80 / 0.4506
Payment = $110.39

Therefore, the amount of each loan payment is $199.94, which is closest to answer choice B.

Question 11

How much should be deposited now if you wish to withdraw $2,000 quarterly in perpetuity? Interest is 3.95% compounded quarterly.

Accepted Answer

The answer of How much should be deposited now if...

Question 12

Calculate the present value of a growing annuity given the following information: annual cash flows = $20,000; cash flow growth rate = 12%; required rate of return = 3%; timeframe = 35 years.

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Question 13

Bandal Corporation wishes to purchase an apartment complex that provides annual cash flows from rental property of $2,000,000. Rental increase is approximated at 2% per year into the foreseeable future. If Bandal's return requirement is 10%, determine the value of the apartment complex.

Accepted Answer

The value of the apartment complex can be calculated using the Gordon Growth Model (a form of the Dividend Discount Model), which is: Value = Cash Flow / (Required Return - Growth Rate). Here, Value = $2,000,000 / (0.10 - 0.02) = $25,000,000.

Question 14

You are comparing two annuities. Both annuities pay the same amount for the same number of months. The discount rate is also identical. If the ordinary annuity is worth $26,500, the annuity due is worth:

Accepted Answer

An annuity due is worth more than an ordinary annuity because payments are received at the beginning of each period. Therefore, the value of an annuity due is the value of the ordinary annuity multiplied by (1 + r).

Question 15

You are expecting annual cash flows of $10,000 in years 1-5; $15,000 in years 6-10; and $25,000 in years 11-25. If the rate of interest is 6% compounded annually, calculate the present value of this cash flow stream.

Accepted Answer

The answer of You are expecting annual cash flows of...

Question 16

Your employer contributes $50 a week to your retirement plan. Assume that you work for your employer for another 12 years and that the applicable discount rate is 8%. Given these assumptions, what is this employee benefit worth to you today?

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Question 17

You are considering a project with the following cash flows:  What is the present value of these cash flows, given a 7.75% discount rate?

Accepted Answer

The answer of You are considering a project with the...

Question 18

You are considering two insurance settlement offers. The first offer includes annual payments of $5,000, $7,500, and $10,000 over the next three years, respectively. The other offer is the payment of one lump sum amount today. You are trying to decide which offer to accept given the fact that your discount rate is 5%. What is the minimum amount that you will accept today if you are to select the lump sum offer?

Accepted Answer

We can calculate the present value of the three annual payments using the formula:

PV = PMT1 / (1 + r) + PMT2 / (1 + r)² + PMT3 / (1 + r)³

where PV is the present value, PMT is the payment in a year, and r is the discount rate.

Substituting the values, we get:

PV = 5,000 / (1 + 0.05) + 7,500 / (1 + 0.05)² + 10,000 / (1 + 0.05)³
PV = $20,203.00

Therefore, the lump sum offer should be at least $20,203.00 to be equivalent to the three annual payments. The answer is B.

Question 19

You have a sub-contracting job with a local manufacturing firm. Your agreement calls for annual payments of $50,000 for the next five years. At a discount rate of 12%, what is this job worth to you today?

Accepted Answer

The present value of an annuity formula is used to calculate the current worth of a series 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 discount rate per period, and n is the number of periods. Plugging in the values: PV = $50,000 * [(1 - (1 + 0.12)^-5) / 0.12], the calculation gives a present value of approximately $180,238.81.

Question 20

What is the present value of the following set of cash flows if the discount rate is 5.25%?

Accepted Answer

The answer of What is the present value of the...

Quiz 6: Discounted Cash Flow Valuation