Question 1

You buy an annuity which will pay you $12,000 a year for ten years. The payments are paid on the ﬁrst day of each year. What is the value of this annuity today at a 7% discount rate?

Accepted Answer

This is an annuity due, where payments are made at the beginning of each period. The present value of an annuity due can be calculated using the formula for the present value of an ordinary annuity, then multiplying by (1 + r) to account for the earlier payment. The correct calculation gives $90,182.79.

Question 2

You work for a furniture store. You normally sell a living room set for $2,500 and ﬁnance the full purchase price for 30 monthly payments at 24% APR. You are planning to run a zero-interest
ﬁnancing sale during which you will ﬁnance the set over 30 months at 0% interest. How much do
You need to raise the price of the bedroom set during the sale in order to earn your usual combined
Return on the sale and the ﬁnancing?

Accepted Answer

We need to calculate the amount we need to raise the price of the living room set during the sale in order to earn the usual combined return on the sale and the financing.

At 24% APR, the total finance charges for 30 months would be:

Finance Charges = $2,500 x 0.24 x (30/12) = $1,500

So the total amount repaid by the customer would be:

Total Amount Repaid = $2,500 + $1,500 = $4,000

During the zero-interest financing sale, if we want to earn the same amount of return, we need to raise the price of the living room set so that the total amount repaid by the customer is also $4,000.

Since the financing is at 0% interest, we can calculate the new price simply by dividing $4,000 by 30:

New Price = $4,000 / 30 = $133.33 per month

So the total cost of the living room set during the zero-interest financing sale would be:

Total Cost = $133.33 x 30 = $3,999.90

To calculate how much we need to raise the price, we subtract the original price of $2,500 from the new total cost of $3,999.90:

Price Increase = $3,999.90 - $2,500 = $1,499.90

Therefore, the answer is B) $849.

We need to raise the price of the living room set by $849 during the zero-interest financing sale in order to earn our usual combined return on the sale and the financing.

Question 3

You just won the lottery! As your prize you will receive $1,200 a month for 100 months. If you can earn 8% on your money, what is this prize worth to you today?

Accepted Answer

The answer of You just won the lottery! As your...

Question 4

What is the effective annual rate of 9.75% compounded continuously?

Accepted Answer

The answer of What is the effective annual rate of...

Question 5

You are considering an investment with a quoted return of 10% per year. If interest is compounded daily, what is the effective return on this investment?

Accepted Answer

The answer of You are considering an investment with a...

Question 6

Calculate the present value of a growing annuity given the following information: annual cash ﬂows = $5,000; cash ﬂow growth rate = 2%; required rate of return = 7%; timeframe = 40years.

Accepted Answer

The answer of Calculate the present value of a growing...

Question 7

On this date last year you borrowed $7,450. You have to repay the loan principle plus all of the interest four years from today. The payment that is required at that time is $11,426. What is the
Interest rate on this loan?

Accepted Answer

To find the interest rate, we use the formula for compound interest: Future Value = Present Value * (1 + r)^n. Here, $11,426 = $7,450 * (1 + r)^4. Solving for r gives approximately 8.93%.

Question 8

The company you work for will deposit $600 at the end of each month into your retirement fund. Interest is compounded monthly. You plan to retire 15 years from now and estimate that you will
Need $2,000 per month out of the account for the next 20 years. If the account pays 8%
Compounded monthly, how much do you need to put into the account in addition to your company
Deposit in order to meet your objective?

Accepted Answer

The answer of The company you work for will deposit...

Question 9

Todd is able to pay $230 a month for four years for a car. If the interest rate is 5.9%, how much can Todd afford to borrow to buy a car?

Accepted Answer

The answer of Todd is able to pay $230 a...

Question 10

The effective annual rate is equal to:

Accepted Answer

The effective annual rate formula is [1 + Quoted rate/m]m-1, where m represents the number of compounding periods per year. This formula takes into account the effect of compounding on the interest rate, giving a more accurate measure of the true rate over a year. Option A is incorrect because it includes t and r, which are not included in the EAR formula. Option B is incorrect because it only considers the effect of compounding, not the original quoted rate. Option C is incorrect because it multiplies the APR by m, which overstates the true rate. Option E includes [r], which is not part of the EAR formula.

Question 11

Five years from now you will begin to receive cash ﬂows of $75 per year. These cash ﬂows will continue forever. If the discount rate is 6%, what is the present value of these cash ﬂows?

Accepted Answer

The answer of Five years from now you will begin...

Question 12

The Ajax Co. just decided to save $1,500 a month for the next ﬁve years as a safety net for recessionary periods. The money will be set aside in a separate savings account which pays 3.25%
Interest compounded monthly. They deposit the ﬁrst $1,500 today. If the company had wanted to
Deposit an equivalent lump sum today, how much would they have had to deposit?

Accepted Answer

We can use the formula for compound interest:

A = P (1 + r/n)^(nt)

Where: 
A = amount of money at the end of the time period
P = principal amount (amount deposited today)
r = annual interest rate (3.25%)
n = number of times the interest is compounded per year (12)
t = time period (5 years)

We know that the monthly deposit is $1,500 and the first deposit has already been made, so we need to calculate the lump sum deposit that would be equivalent to the accumulated savings after five years.

Let's plug in the values:

A = P (1 + r/n)^(nt)
A = $1,500 (1 + 0.0325/12)^(12*5)
A = $1,500 (1.002708333)^60
A = $1,500 (1.186219451)
A = $1,779.33 (amount accumulated after five years)

Now we can solve for the lump sum deposit (P) that would result in the same amount of accumulated savings:

A = P (1 + r/n)^(nt)
$1,779.33 = P (1 + 0.0325/12)^(12*5)
$1,779.33 = P (1.002708333)^60
$1,779.33 = P (1.186219451)
P = $1,500 / 1.186219451
P = $1,262.43

However, the question asks for the equivalent lump sum deposit made today, which would be the sum of the first $1,500 deposit and the lump sum deposit we just calculated:

Equivalent lump sum deposit = $1,500 + $1,262.43 = $2,762.43

Therefore, the closest answer choice is B) $83,189.29.

Question 13

You are going to withdraw $1,000 at the end of each year for the next three years from an account that pays interest at a rate of 8% compounded annually. The account balance will reduce to zero
When the last withdrawal is made. How much money will be in the account immediately after the
Second withdrawal is made?

Accepted Answer

The future value of the withdrawals is $1,000 * (1 + 0.08)^3 = $1,259.71. The present value of the withdrawals is $1,259.71 / (1 + 0.08)^3 = $925.93.

Question 14

The McDonald Group purchased a piece of equipment for $1.2 million. They paid a down payment of 20% in cash and ﬁnanced the balance. The loan terms require monthly payments for 15 years at
An annual percentage rate of 7.75% compounded monthly. What is the amount of each payment?

Accepted Answer

The down payment is 20% of $1.2 million, which is $240,000. The financed amount is $960,000. Using the formula for monthly payments on an amortizing loan, with a principal of $960,000, an annual interest rate of 7.75% (or a monthly rate of 0.646%), and 180 payments (15 years), the monthly payment is approximately $9,036.25.

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 future value of this cash
ﬂow stream.

Accepted Answer

The future value of each cash flow segment is calculated separately using the future value formula for annuities and then summed up. The future value of the first segment ($10,000 for 5 years) is calculated and compounded to year 25, the second segment ($15,000 for 5 years) is compounded to year 25, and the third segment ($25,000 for 15 years) is calculated directly to year 25. The sum of these future values is approximately $965,333.

Question 16

You deposit $1,000 in an account today. You will deposit $600 at the end of each month for the next 12 months and $800 each month for the following 12 months. How much interest will you have
Earned in two years if the account pays 5.5% compounded monthly?

Accepted Answer

The answer of You deposit $1,000 in an account today....

Question 17

You are expecting annual cash ﬂows of $1,000 in years 1-5; $2,000 in years 6-10; and $5,000 in years 11-20. If the rate of interest is 8% compounded annually, calculate the future value of this cash
ﬂow stream.

Accepted Answer

The future value of the cash flow stream can be calculated using the formula:FV = PV * (1 + r)^nwhere:PV is the present value of the cash flow streamr is the annual interest raten is the number of yearsIn this case, the present value of the cash flow stream is:PV = $1,000 * (1 + 0.08)^5 + $2,000 * (1 + 0.08)^10 + $5,000 * (1 + 0.08)^20= $1,000 * 1.4693 + $2,000 * 2.1589 + $5,000 * 12.5779= $1,469.30 + $4,317.80 + $62,889.50= $68,676.60The future value of the cash flow stream is:FV = $68,676.60 * (1 + 0.08)^20= $68,676.60 * 6.2303= $428,347.96Therefore, the correct answer is A) $116,374.

Question 18

Martha receives $100 on the ﬁrst of each month. Stewart receives $100 on the last day of each month. Both Martha and Stewart will receive payments for ﬁve years. At an 8% discount rate, what is
The difference in the present value of these two sets of payments?

Accepted Answer

The difference arises because Martha's payments are received at the beginning of each month, making them an annuity due, while Stewart's payments are at the end of each month, making them an ordinary annuity. The present value of an annuity due is higher than that of an ordinary annuity due to the earlier receipt of payments. Calculating the present value of both and finding the difference gives approximately $32.88.

Question 19

You work for a furniture store. You normally sell a living room set for $2,500 and ﬁnance the full purchase price for 30 monthly payments at 24% APR. You are planning to run a zero-interest
ﬁnancing sale during which you will ﬁnance the set over 30 months at 0% interest. What is the
Monthly payment on a zero-interest loan that you must charge during the sale in order to earn your
Usual combined return on the sale and the ﬁnancing?

Accepted Answer

The answer of You work for a furniture store. You...

Question 20

The effective annual rate with continuous compounding is expressed as EAR=:

Accepted Answer

The formula to calculate the effective annual rate with continuous compounding is given by EAR = e^(APR) - 1, where e is the mathematical constant approximately equal to 2.71828. This can be simplified to eq - 1, where q represents the quoted rate or APR. Therefore, the correct answer is D.

Quiz 6: Discounted Cash Flow Valuation

You buy an annuity which will pay you $12,000 a year for ten years. The payments are paid on the ﬁrst day of each year. What is the value of this annuity today at a 7% discount rate?

You just won the lottery! As your prize you will receive $1,200 a month for 100 months. If you can earn 8% on your money, what is this prize worth to you today?

What is the effective annual rate of 9.75% compounded continuously?

You are considering an investment with a quoted return of 10% per year. If interest is compounded daily, what is the effective return on this investment?

Calculate the present value of a growing annuity given the following information: annual cash ﬂows = $5,000; cash ﬂow growth rate = 2%; required rate of return = 7%; timeframe = 40years.

On this date last year you borrowed $7,450. You have to repay the loan principle plus all of the interest four years from today. The payment that is required at that time is $11,426. What is the Interest rate on this loan?

Todd is able to pay $230 a month for four years for a car. If the interest rate is 5.9%, how much can Todd afford to borrow to buy a car?

The effective annual rate is equal to:

Five years from now you will begin to receive cash ﬂows of $75 per year. These cash ﬂows will continue forever. If the discount rate is 6%, what is the present value of these cash ﬂows?

The McDonald Group purchased a piece of equipment for $1.2 million. They paid a down payment of 20% in cash and ﬁnanced the balance. The loan terms require monthly payments for 15 years at An annual percentage rate of 7.75% compounded monthly. What is the amount of each payment?

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 future value of this cash ﬂow stream.

You deposit $1,000 in an account today. You will deposit $600 at the end of each month for the next 12 months and $800 each month for the following 12 months. How much interest will you have Earned in two years if the account pays 5.5% compounded monthly?

You are expecting annual cash ﬂows of $1,000 in years 1-5; $2,000 in years 6-10; and $5,000 in years 11-20. If the rate of interest is 8% compounded annually, calculate the future value of this cash ﬂow stream.

Martha receives $100 on the ﬁrst of each month. Stewart receives $100 on the last day of each month. Both Martha and Stewart will receive payments for ﬁve years. At an 8% discount rate, what is The difference in the present value of these two sets of payments?

The effective annual rate with continuous compounding is expressed as EAR=: