Question 1

If a 5-year regular annuity has a present value of $1,000,and if the interest rate is 10 percent,what is the amount of each annuity payment?

Accepted Answer

Using the formula for the present value of an annuity:

PV = Payment × [(1 - (1 / (1 + r)n)) / r]

where PV = present value, Payment = amount of each annuity payment, r = interest rate, and n = number of payments

Substituting the given values:

$1,000 = Payment × [(1 - (1 / (1 + 0.10)5)) / 0.10]

Solving for Payment:

Payment = $263.80 (rounded to the nearest penny)

Question 2

You just graduated,and you plan to work for 10 years and then to leave for the Australian "Outback" bush country.You figure you can save $1,000 a year for the first 5 years and $2,000 a year for the next 5 years.These savings cash flows will start one year from now.In addition,your family has just given you a $5,000 graduation gift.If you put the gift now,and your future savings when they start,into an account which pays 8 percent compounded annually,what will your financial "stake" be when you leave for Australia 10 years from now?

Accepted Answer

To calculate the future value of the savings and the graduation gift, we use the future value formula for a series of cash flows and a single lump sum.1. The $5,000 gift is invested now, so it has 10 years to grow at 8% compounded annually.   Future Value (FV) of the gift = $5,000 * (1 + 0.08)^10 = $10,794.622. For the $1,000 annual savings for the first 5 years, we use the future value of an annuity formula. These savings will have 5 years to grow after the last deposit.   FV of $1,000 savings = $1,000 * [(1 + 0.08)^5 - 1] / 0.08 = $5,866.603. For the $2,000 annual savings for the next 5 years, we use the future value of an annuity formula again. These savings will have no time to grow after the last deposit since it's at the end of the 10 years.   FV of $2,000 savings = $2,000 * [(1 + 0.08)^5 - 1] / 0.08 = $11,733.204. Add the future values together to get the total financial stake:   Total = $10,794.62 (gift) + $5,866.60 (first 5 years savings) + $11,733.20 (next 5 years savings) = $28,394.42The closest answer to our calculation is $28,393, so there might be a slight rounding difference in the calculation process. However, the correct choice based on the closest match is:B

Question 3

Assume you are to receive a 20-year annuity with annual payments of $50.The first payment will be received at the end of Year 1,and the last payment will be received at the end of Year 20.You will invest each payment in an account that pays 10 percent.What will be the value in your account at the end of Year 30?

Accepted Answer

The answer of Assume you are to receive a 20-year...

Question 4

What is the future value of a 5-year ordinary annuity with annual payments of $200,evaluated at a 15 percent interest rate?

Accepted Answer

The answer of What is the future value of a...

Question 5

A recent advertisement in the financial section of a magazine carried the following claim: "Invest your money with us at 14 percent,compounded annually,and we guarantee to double your money sooner than you imagine." Ignoring taxes,how long would it take to double your money at a simple rate of 14 percent,compounded annually?

Accepted Answer

To double your money at a simple rate of 14 percent, compounded annually, it would take approximately 5 years. This is calculated using the Rule of 72, which states that if you divide the number 72 by the annual rate (in this case, 14 percent), you will get the approximate number of years it takes for the investment to double. 72/14 = 5.14. Therefore, the best answer is B - approximately 5 years.

Question 6

In 1958 the average tuition for one year at an Ivy League school was $1,800.Thirty years later,in 1988,the average cost was $13,700.What was the growth rate in tuition over the 30-year period?

Accepted Answer

The answer of In 1958 the average tuition for one...

Question 7

You want to buy a Nissan 350Z on your 27th birthday.You have priced these cars and found that they currently sell for $30,000.You believe that the price will increase by 5 percent per year until you are ready to buy.You can presently invest to earn 14 percent.If you just turned 20 years old,how much must you invest at the end of each of the next 7 years to be able to purchase the Nissan in 7 years?

Accepted Answer

The cost of the car in 7 years will be $30,000*(1.05)^7 = $41,513.83.

To find out how much to invest annually, we can use the present value of an annuity formula:

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

where PMT is the payment (or investment) at the end of each year, PV is the present value (or amount we need in 7 years), r is the annual interest rate, and n is the number of periods (years).

Using our values:

PV = $41,513.83 
r = 14% = 0.14 
n = 7

PMT = ($41,513.83 * 0.14) / ((1 + 0.14)^7 - 1) 
PMT = $3,933.93

So we need to invest $3,933.93 at the end of each year for the next 7 years to be able to purchase the Nissan 350Z on our 27th birthday. Therefore, the answer is B.

Question 8

Assume that you will receive $2,000 a year in Years 1 through 5,$3,000 a year in Years 6 through 8,and $4,000 in Year 9,with all cash flows to be received at the end of the year.If you require a 14 percent rate of return,what is the present value of these cash flows?

Accepted Answer

We can use the present value formula for each set of cash flows and add them together:

PV of Years 1-5 = $2,000(PVIFA14%,5) = $2,000(3.433) = $6,866

PV of Years 6-8 = $3,000(PVIFA14%,3) = $3,000(2.407) = $7,221

PV of Year 9 = $4,000/(1.14^9) = $1,901

Total PV = $6,866 + $7,221 + $1,901 = $11,988

Therefore, the closest option is C) $11,714.

Question 9

At approximately what rate would you have to invest a lump-sum amount today if you need the amount to triple in six years? Assume interest is compounded annually.

Accepted Answer

The answer of At approximately what rate would you have...

Question 10

If $100 is placed in an account that earns a simple 4 percent,compounded quarterly,what will it be worth in 5 years?

Accepted Answer

Using the formula for simple interest compounded quarterly, we get:

A = P(1 + (r/n))^(nt)
where A is the amount after time t, P is the principal ($100 in this case), r is the interest rate (4% as a decimal), n is the number of times compounded per time period (4 quarters in a year), and t is the number of time periods (5 years).

Plugging in the values, we get:

A = 100(1 + (0.04/4))^(4*5)
A = 100(1.01)^20
A = $122.02

Therefore, the answer is choice A.

Question 11

Which of the following statements is most correct?

Accepted Answer

- A is true because with a lower interest rate, a larger portion of the payment goes towards the principal rather than interest. - B is true because the effective interest rate of a 10% simple rate with semiannual payments is higher than a 10.1% rate with annual payments, making it preferable for a lender but not for a borrower. - C is true because as the discount rate approaches zero, the present value of the perpetuity (which is calculated as the annual payment divided by the discount rate) approaches infinity.

Question 12

As the winning contestant in a television game show,you are considering the prizes to be awarded.You must indicate to the sponsor which of the following two choices you prefer,assuming you want to maximize your wealth.Assume it is now January 1,and there is no danger whatever that the sponsor won't pay off.  Which one would you choose?

Accepted Answer

Choice 1 offers a lump sum payment of $1,000,000 immediately. This is the preferred choice as it offers the highest immediate wealth and there is no indication that the sponsor will not pay off. Choice 2 offers 20 annual payments of $75,000 each, resulting in a total payout of $1,500,000. However, the present value of this option is less than $1,000,000 due to the time value of money and the uncertainty of receiving future payments.

Question 13

Sarah is thinking about purchasing an investment from HiBond Investing.If she buys the investment,Sarah will receive $100 every three months for five years.The first $100 payment will be made as soon as she purchases the investment.If Sarah's required rate of return is 16 percent,to the nearest dollar,how much should she be willing to pay for this investment?

Accepted Answer

To calculate how much Sarah should be willing to pay for the investment, we need to use the concept of present value of future cash flows.

Since Sarah will receive $100 every three months for five years, that's a total of 20 payments ($100 x 20 = $2,000).

We can use the formula:

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

Where: 
PV = Present value 
C = Cash flow 
r = Required rate of return (in decimal form) 
n = Number of periods

Plugging in the values, we get:

PV = $100 x (1 - (1+.16/4)^-20) / (.16/4)

PV = $1,413

So Sarah should be willing to pay $1,413 for this investment.

The Answer is (B).

Question 14

At an inflation rate of 9 percent,the purchasing power of $1 would be cut in half in 8.04 years.How long to the nearest year would it take the purchasing power of $1 to be cut in half if the inflation rate were only 4%?

Accepted Answer

We can use the formula for the time it takes for purchasing power to be halved:

t = ln(2) / ln(1 + r)

where r is the inflation rate as a decimal.

For an inflation rate of 9%, we have:

t = ln(2) / ln(1 + 0.09) ≈ 8.04 years

For an inflation rate of 4%, we have:

t = ln(2) / ln(1 + 0.04) ≈ 17.67 years

Rounding to the nearest year, we get:

Answer: C) 18 years

Question 15

At an effective annual interest rate of 20 percent,how many years will it take a given amount to triple in value? (Round to the closest year.)

Accepted Answer

Using the formula for compound interest: 
FV = PV(1 + r/n)^(nt)
where FV is the future value, PV is the present value, r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the number of years. We want to find t when FV/PV = 3 and r = 0.2 (20%) so the equation simplifies to:
3 = 1(1 + 0.2/1)^(1t)
Taking the natural log of both sides:
ln 3 = t ln (1.2)
t = ln 3 / ln (1.2)
t ≈ 5.65
Rounding to the nearest year, we get 6 years. Therefore, the answer is C.

Question 16

You deposited $1,000 in a savings account that pays 8 percent interest,compounded quarterly,planning to use it to finish your last year in college.Eighteen months later,you decide to go to the Rocky Mountains to become a ski instructor rather than continue in school,so you close out your account.How much money will you receive?

Accepted Answer

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. In this case, P = $1,000, r = 0.08 (8%), n = 4 (since the interest is compounded quarterly), and t = 1.5 years (18 months). Plugging these values into the formula gives A = 1000(1 + 0.08/4)^(4*1.5) = $1,126. Therefore, the correct answer is $1,126.

Question 17

Gomez Electronics needs to arrange financing for its expansion program.Bank A offers to lend Gomez the required funds on a loan where interest must be paid monthly,and the quoted rate is 8 percent.Bank B will charge 9 percent,with interest due at the end of the year.What is the difference in the effective annual rates charged by the two banks?

Accepted Answer

The answer of Gomez Electronics needs to arrange financing for...

Question 18

Assume that you can invest to earn a stated annual rate of return of 12 percent,but where interest is compounded semiannually.If you make 20 consecutive semiannual deposits of $500 each,with the first deposit being made today,what will your balance be at the end of Year 20?

Accepted Answer

The answer of Assume that you can invest to earn...

Question 19

You expect to receive $1,000 at the end of each of the next 3 years.You will deposit these payments into an account which pays 10 percent compounded semiannually.What is the future value of these payments,that is,the value at the end of the third year?

Accepted Answer

We can use the formula for the future value of an annuity with semi-annual compounding: 
FV = PMT [((1 + r/n)^nt - 1)/(r/n)]
where PMT is the payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, PMT = $1,000, r = 10%, n = 2 (since compounding is semi-annual), and t = 3.

FV = $1,000 [((1 + 0.10/2)^(2*3) - 1)/(0.10/2)]
FV = $1,000 [(1.05^6 - 1)/0.05]
FV = $1,000 [10.5302]
FV = $3,318.02

Therefore, the best choice is C, which is the closest answer to $3,318.

Question 20

You have the opportunity to buy a perpetuity which pays $1,000 annually.Your required rate of return on this investment is 15 percent.You should be essentially indifferent to buying or not buying the investment if it were offered at a price of

Accepted Answer

To calculate the price at which we would be indifferent to buying or not buying the perpetuity, we use the formula Price = Annual Payment / Required Rate of Return. Plugging in the values, we get Price = $1,000 / 0.15 = $6,666.67. Therefore, at a price of $6,666.67 or lower, we would want to buy the perpetuity, and at a price higher than $6,666.67, we would not want to buy it. Therefore, the best choice is C.

Quiz 4: The Time Value of Money