Question 1

Your insurance agent is trying to sell you an annuity that costs $100,000 today. By buying this annuity, your agent promises that you will receive payments of $384.40 a month for the next 40
Years. What is the rate of return on this investment?

Accepted Answer

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Question 2

Your insurance agent is trying to sell you an annuity that costs $165,000 today. By buying this annuity, your agent promises that you will receive payments of $775 a month for the next 40 years.
What is the rate of return on this investment?

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Question 3

An insurance company is offering monthly payments of $250 for the next twenty years in exchange for a one-time payment of $40,000 today. What is the rate of return on this offer?

Accepted Answer

To find the rate of return, we need to calculate the present value of the monthly payments and compare it to the initial investment of $40,000. 
Using a financial calculator or formula, we can find that the present value of the monthly payments is $44,645. 
Then, we can use the formula (future value / present value)^(1/N) - 1, where N is the number of years, to find the rate of return. 
Plugging in the numbers, we get: 
(44,645 / 40,000)^(1/20) - 1 = 0.0436 or 4.36%
Therefore, option B is the best choice.

Question 4

Poor Dog, Inc. borrowed $135,000 from the bank today. They must repay this money over the next six years by making monthly payments of $2,215.10. What is the interest rate on the loan?

Accepted Answer

The interest rate can be found by using the formula for the monthly payment (PMT) of an annuity: PMT = P[r(1 + r)^n] / [(1 + r)^n - 1], where P is the principal amount ($135,000), PMT is the monthly payment ($2,215.10), n is the total number of payments (6 years * 12 months = 72 payments), and r is the monthly interest rate. Solving this equation for r requires either iterative methods or a financial calculator. Plugging the given values into a financial calculator or an appropriate financial function in a spreadsheet yields an interest rate close to 5.65% annually.

Question 5

A house in Vancouver that was purchased 30 years ago for $250,000 recently sold for $1.5 million. Calculate the annual rate of return for this investment.

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Question 6

You have $10,000 to invest. The First National Bank offers one-year certiﬁcates of deposit with a stated rate of 5.50% compounded quarterly. What rate compounded semi-annually would provide
You with the same amount of money at the end of one year?

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Question 7

Baker Industries has been investing $115,000 a year for the past 5 years into a business venture. Today, Baker sold that venture for $1.2 million. What is the rate of return on this venture?

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Question 8

Ottawa Manor would like to buy some additional land and build a new assisted living center. The anticipated total cost is $12.4 million. The CEO of the ﬁrm is quite conservative and will only do this
When the company has suﬃcient funds to pay cash for the entire construction project. Management
Has decided to save $235,000 a month for this purpose. The ﬁrm earns 7% compounded monthly
On the funds it saves. How long does the company have to wait before expanding its operations?

Accepted Answer

We need to find out how long it takes to save enough money to pay for the construction project, which costs $12.4 million.

We know that the company is saving $235,000 a month and earning 7% compounded monthly on those savings. The formula we can use to calculate the future value of an annuity is:

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

Where:
FV = future value
PMT = monthly payment
r = interest rate per month
n = number of months

Plugging in the numbers we know:

FV = $12.4 million
PMT = $235,000
r = 0.07/12
n = ?

$12.4 million = $235,000 x [(1 + 0.07/12)^n - 1] / (0.07/12)

Solving for n:

n = ln[(12.4 million x 0.07/12) / (235,000 x 0.07/12 + 0.07/12)] / ln(1 + 0.07/12)

n = 46.14 months

Therefore, the company has to wait for 46.14 months before expanding its operations.

Question 9

What continuously compounded rate of return allows you to triple your money in 20 years?

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Question 10

Today, you signed loan papers agreeing to borrow $7,500 at 9% compounded monthly. The loan payment is $196.99 a month. How many loan payments must you make before the loan is paid in
Full?

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Question 11

After winning the lottery, you are indifferent between receiving $750,000 end-of-the-year payments for 15 years or a lump-sum payment of $7,106,223 today. At what interest rate would you be
Indifferent between the two options?

Accepted Answer

To find the interest rate that makes the lottery winner indifferent between the two options, we can use the present value formula:

PV = PMT x (1 - (1 + r)^-n) / r

Where PV is the present value of the end-of-the-year payments, PMT is the annual payment, r is the interest rate, and n is the number of years.

For the first option, we have:

PV = 750,000 x (1 - (1 + r)^-15) / r

For the second option, we have:

PV = 7,106,223

Since the winner is indifferent between the two options, we know that the present values must be equal:

750,000 x (1 - (1 + r)^-15) / r = 7,106,223

Solving for r using a financial calculator or software, we get r = 6.38%.

Therefore, the best choice would be to take the lump-sum payment of $7,106,223 today.

Question 12

Fast Eddie's Used Cars will sell you a 2000 Ford Taurus for $3,000 with no money down. You agree to make weekly payments of $40 for two years, beginning one week after you buy the car. What is
The EAR of this loan?

Accepted Answer

The EAR (Effective Annual Rate) can be calculated using the formula for the interest rate of an annuity. The loan amount is $3,000, with weekly payments of $40 for 104 weeks (2 years). Solving for the interest rate using the annuity formula and converting it to EAR gives approximately 40.94%.

Question 13

Today, you signed loan papers agreeing to borrow $4,954.85 at 9% compounded monthly. The loan payment is $143.84 a month. How many loan payments must you make before the loan is paid in
Full?

Accepted Answer

The correct answer is D.The number of loan payments can be calculated using the formula:N = -(log(1 - (r * P) / PMT) / log(1 + r))where:N is the number of loan paymentsr is the monthly interest rate (9% / 12 = 0.0075)P is the principal amount ($4,954.85)PMT is the monthly payment ($143.84)Plugging in the values, we get:N = -(log(1 - (0.0075 * 4954.85) / 143.84) / log(1 + 0.0075))N = 36.00Therefore, the number of loan payments required to pay off the loan in full is 36.

Question 14

You currently have $185,000 in an interest-earning account, and from this account you wish to withdraw $15,000 annually for 25 years. What annual rate of return must you make on this account
To meet your objective?

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Question 15

You just won the lottery. You and your heirs will receive $25,000 per year forever, beginning one year from now. If the present value of the lottery is $416,667, what is the discount rate used to value
This perpetuity?

Accepted Answer

The present value of a perpetuity can be calculated using the following formula: PV = PMT / r, where PV is the present value, PMT is the amount of the payment each period (in this case, $25,000 per year), and r is the discount rate. Plugging in the numbers given, we get:

416,667 = 25,000 / r

Solving for r, we get r = 6.0%. Therefore, the discount rate used to value this perpetuity is 6.0%.

Question 16

What is the annual percentage rate on a loan with a stated rate of 2% per quarter?

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Question 17

Your mother helped you start saving $25 a month beginning on your 10th birthday. She always made you make your deposit on the ﬁrst day of each month just to "start the month out right".
Today, you turn 21 and have $4,482.66 in your account. What is your rate of return on your savings?

Accepted Answer

The amount saved from age 10 to age 21 is 11 years × 12 months/year × $25/month = $3,300. 
So, the interest earned is $4,482.66 − $3,300 = $1,182.66.
Using the compound interest formula: 
$1,182.66 = $3,300 × (1 + r)n 
where r is the annual interest rate and n is the number of years (11). 
Solving for r, we get r ≈ 0.0529 or 5.29%. 
Therefore, the answer is B) 5.29%.

Question 18

Your father won a lottery years ago. The value of his winnings at the time was $225,000. He invested this money such that it will provide annual payments of $12,000 a year to his heirs forever.
What is the rate of return?

Accepted Answer

The rate of return is the interest rate that would make the present value of the payments equal to the initial investment. Using a financial calculator, the present value of perpetual payments of $12,000 at a rate of 5.33% is $225,000, which matches the initial investment. Therefore, the rate of return is 5.33%.

Question 19

At what rate of interest (compounded monthly) will quarterly payments of $2,000 accumulate to $25,000 in three years?

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Question 20

The Eternal Gift Insurance Company is offering you a policy that will pay you and your heirs $10,000 a year forever. The cost of the policy is $285,000. What is the rate of return on this policy?

Accepted Answer

To find the rate of return on the policy, we need to divide the annual payment ($10,000) by the initial cost of the policy ($285,000).

Rate of return = (Annual payment/Initial cost) x 100%
Rate of return = ($10,000/$285,000) x 100%
Rate of return = 0.0351 or 3.51%

Therefore, the rate of return on the policy is 3.51%. The best choice based on this calculation is D.

Quiz 6: Discounted Cash Flow Valuation

Your insurance agent is trying to sell you an annuity that costs $100,000 today. By buying this annuity, your agent promises that you will receive payments of $384.40 a month for the next 40 Years. What is the rate of return on this investment?

Your insurance agent is trying to sell you an annuity that costs $165,000 today. By buying this annuity, your agent promises that you will receive payments of $775 a month for the next 40 years. What is the rate of return on this investment?

An insurance company is offering monthly payments of $250 for the next twenty years in exchange for a one-time payment of $40,000 today. What is the rate of return on this offer?

Poor Dog, Inc. borrowed $135,000 from the bank today. They must repay this money over the next six years by making monthly payments of $2,215.10. What is the interest rate on the loan?

A house in Vancouver that was purchased 30 years ago for $250,000 recently sold for $1.5 million. Calculate the annual rate of return for this investment.

You have $10,000 to invest. The First National Bank offers one-year certiﬁcates of deposit with a stated rate of 5.50% compounded quarterly. What rate compounded semi-annually would provide You with the same amount of money at the end of one year?

Baker Industries has been investing $115,000 a year for the past 5 years into a business venture. Today, Baker sold that venture for $1.2 million. What is the rate of return on this venture?

What continuously compounded rate of return allows you to triple your money in 20 years?

Today, you signed loan papers agreeing to borrow $7,500 at 9% compounded monthly. The loan payment is $196.99 a month. How many loan payments must you make before the loan is paid in Full?

After winning the lottery, you are indifferent between receiving $750,000 end-of-the-year payments for 15 years or a lump-sum payment of $7,106,223 today. At what interest rate would you be Indifferent between the two options?

Fast Eddie's Used Cars will sell you a 2000 Ford Taurus for $3,000 with no money down. You agree to make weekly payments of $40 for two years, beginning one week after you buy the car. What is The EAR of this loan?

Today, you signed loan papers agreeing to borrow $4,954.85 at 9% compounded monthly. The loan payment is $143.84 a month. How many loan payments must you make before the loan is paid in Full?

You currently have $185,000 in an interest-earning account, and from this account you wish to withdraw $15,000 annually for 25 years. What annual rate of return must you make on this account To meet your objective?

You just won the lottery. You and your heirs will receive $25,000 per year forever, beginning one year from now. If the present value of the lottery is $416,667, what is the discount rate used to value This perpetuity?

What is the annual percentage rate on a loan with a stated rate of 2% per quarter?

Your mother helped you start saving $25 a month beginning on your 10th birthday. She always made you make your deposit on the ﬁrst day of each month just to "start the month out right". Today, you turn 21 and have $4,482.66 in your account. What is your rate of return on your savings?

Your father won a lottery years ago. The value of his winnings at the time was $225,000. He invested this money such that it will provide annual payments of $12,000 a year to his heirs forever. What is the rate of return?

At what rate of interest (compounded monthly) will quarterly payments of $2,000 accumulate to $25,000 in three years?

The Eternal Gift Insurance Company is offering you a policy that will pay you and your heirs $10,000 a year forever. The cost of the policy is $285,000. What is the rate of return on this policy?