Question 1

Which of the following statements is correct?

Accepted Answer

This statement is known as the annuity due rule, which states that the future value of an annuity due is equal to the future value of an otherwise identical regular annuity with interest compounded on each payment for one additional period. This is because with an annuity due, each payment is received at the beginning of the period and immediately starts earning interest, whereas with a regular annuity, each payment is received at the end of the period and does not earn interest until the following period. The other statements are incorrect.

Question 2

Suppose someone offered you your choice of two equally risky annuities,each paying $5,000 per year for 5 years.One is an annuity due,while the other is a regular (or deferred)annuity.If you are a rational wealth-maximizing investor which annuity would you choose?

Accepted Answer

The annuity due would be the better choice because it allows for immediate payments, resulting in a higher present value compared to the deferred annuity. The time value of money dictates that money received earlier is worth more than money received later, assuming the same interest rate. Therefore, the annuity due would have a higher present value and be the better choice for a rational wealth-maximizing investor. Option E is also correct, but it is important to note that the doubling of payments changes the comparison between the two annuities.

Question 3

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

E

Question 4

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 5

As the discount rate increases without limit,the present value of the future cash inflows

Accepted Answer

As the discount rate increases without limit, the present value of future cash inflows approaches zero. This is because a higher discount rate reduces the value of future cash flows, making them less valuable in today's dollars. Eventually, the discount rate becomes so high that the present value of future cash flows approaches zero.

Question 6

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

Accepted Answer

The present value of an ordinary annuity is calculated as follows:PV = PMT * [1 - (1 + r)^-n] / rwhere:PMT = the annual paymentr = the interest raten = the number of yearsIn this case, PMT = $200, r = 15%, and n = 5. Plugging these values into the formula, we get:PV = $200 * [1 - (1 + 0.15)^-5] / 0.15PV = $200 * [1 - 0.5674] / 0.15PV = $200 * 0.4326 / 0.15PV = $670.43Therefore, the present value of the annuity is $670.43.

Question 7

Which of the following statements is correct?

Accepted Answer

The answer of Which of the following statements is correct?
...

Question 8

Supposed someone offered you the choice of two equally risky annuities,each paying $10,000 per year for five years.One is an ordinary (or deferred)annuity,the other is an annuity due.Which of the following statements is most correct?

Accepted Answer

The present value of an annuity due is always greater than the present value of an ordinary annuity because the cash flows are received one period earlier, resulting in the extra period of compounding. The future value of an annuity due will also be greater than the future value of an ordinary annuity because of this extra period of compounding. Interest rate changes will affect both annuities equally, so answer choice D is incorrect. Answer choice A is incorrect because both the present value and future value of the annuity due are greater than those of the ordinary annuity.

Question 9

Which of the following statements is most correct?

Accepted Answer

When annual compounding is used, the effective annual rate (EAR) does indeed equal the nominal or stated rate (simple rate), because there is no compounding within the year to increase the effective yield. Additionally, since the compounding period is annual, the periodic rate (the rate for each compounding period) also equals the nominal rate, as there is only one period per year. Therefore, both statements A and B are correct, making D the most correct choice.

Question 10

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 11

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

To triple in value means the amount will increase by a factor of 3. 
Using the formula for compound interest: FV = PV(1+i)^n, where FV is the future value, PV is the present value, i is the interest rate, and n is the number of compounding periods: 
3 = 1*(1+0.20)^n 
Taking the natural log of both sides: 
ln(3) = n*ln(1.20) 
n = ln(3)/ln(1.20) = 5.65 years. 
Rounding to the nearest year: 
it will take 6 years for the amount to triple in value. 
Therefore, the answer is C.

Question 12

Which of the following statements is correct?

Accepted Answer

The answer of Which of the following statements is correct?
...

Question 13

A $10,000 loan is to be amortized over 5 years,with annual end-of-year payments.Given the following facts,which of these statements is correct?

Accepted Answer

The proportion of each payment that represents interest increases with the interest rate because the total amount of interest paid on each payment increases with the interest rate, while the principal repayment portion would adjust accordingly to ensure the loan is amortized over the specified period.

Question 14

Given some amount to be received several years in the future,if the interest rate increases,the present value of the future amount will

Accepted Answer

When the interest rate increases, the present value of future amounts decreases. This is because a higher interest rate means that you could receive a higher return by investing your money elsewhere, so the value of the future amount decreases.

Question 15

Which of the following statements is correct?

Accepted Answer

Statement C is correct because in an amortized loan, the total payment amount per period remains constant, but the composition of the payment changes over time. Early in the loan's life, a larger portion of the payment is applied toward interest. As the loan matures, the interest portion decreases while the principal portion increases.

Question 16

Which of the following statements is false?

Accepted Answer

All the statements provided are true based on the principles of time value of money and the basic concepts of finance.

Question 17

Which of the following statements is correct?

Accepted Answer

The present value of a future sum decreases as the interest rate or the number of discount periods per year increases because a higher interest rate or more frequent compounding (more discount periods) means a higher discount factor applied to the future sum, thus reducing its present value.

Question 18

If you presently have $6,000 invested at a rate of 15 percent,how many years will it take for your investment to triple? (Round up to obtain a whole number of years if necessary. )

Accepted Answer

Using the Rule of 72, you can estimate the number of years to triple an investment by dividing 72 by the annual interest rate. 72 / 15 ≈ 4.8 years to double, and approximately 8 years to triple.

Question 19

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

Using the rule of 72 (where 72 divided by the interest rate equals the number of years to double your money), we get 72/14 = 5.14. Therefore, it would take approximately 5 years to double your money at a simple rate of 14 percent compounded annually.

Question 20

You have determined the profitability of a planned project by finding the present value of all the cash flows form that project.Which of the following would cause the project to look more appealing in terms of the present value of those cash flows?

Accepted Answer

A decrease in the discount rate increases the present value of future cash flows, making the project more appealing.

Quiz 9: Time Value of Money

Which of the following statements is correct?

Suppose someone offered you your choice of two equally risky annuities,each paying $5,000 per year for 5 years.One is an annuity due,while the other is a regular (or deferred) annuity.If you are a rational wealth-maximizing investor which annuity would you choose?

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

Which of the following statements is most correct?

As the discount rate increases without limit,the present value of the future cash inflows

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

Which of the following statements is correct?

Supposed someone offered you the choice of two equally risky annuities,each paying $10,000 per year for five years.One is an ordinary (or deferred) annuity,the other is an annuity due.Which of the following statements is most correct?

Which of the following statements is most correct?

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. )

Which of the following statements is correct?

A $10,000 loan is to be amortized over 5 years,with annual end-of-year payments.Given the following facts,which of these statements is correct?

Given some amount to be received several years in the future,if the interest rate increases,the present value of the future amount will

Which of the following statements is correct?

Which of the following statements is false?

Which of the following statements is correct?

If you presently have $6,000 invested at a rate of 15 percent,how many years will it take for your investment to triple? (Round up to obtain a whole number of years if necessary. )

You have determined the profitability of a planned project by finding the present value of all the cash flows form that project.Which of the following would cause the project to look more appealing in terms of the present value of those cash flows?