Question 1

All else equal, a dollar received sooner is worth more than a dollar received at some later date, because the sooner the dollar is received the more quickly it can be invested to earn a positive return.

Accepted Answer

This statement is true according to the principle of time value of money. The earlier a dollar is received, the longer it can be invested and earn a positive return, increasing its present value. This is why investments that offer higher rates of return over shorter periods of time are more valuable than investments that offer the same rate of return over longer periods of time.

Question 2

The effective annual rate is always greater than the simple rate as a result of compounding effects.

Accepted Answer

False

Question 3

When a loan is amortized, the largest portion of the periodic payment goes to reduce principal in the early years of the loan such that the accumulated interest can be spread out over the life of the loan.

Accepted Answer

In the early years of an amortized loan, the largest portion of the periodic payment is typically allocated towards interest, not principal. As time progresses, the portion of the payment going towards the principal increases.

Question 4

Compounding is the process of converting today's values, which are termed present value, to future value.

Accepted Answer

Compounding involves calculating the future value of a present value, adding interest earned over time.

Question 5

The difference between the PV of an annuity due and the PV of an ordinary annuity is that each of the payments of the annuity due is discounted by one more year.

Accepted Answer

This is because in an annuity due, the first payment is made immediately at the beginning of the period, whereas in an ordinary annuity, the first payment is made at the end of the period. Therefore, the payments in an annuity due are discounted for one additional year compared to an ordinary annuity.

Question 6

Because we usually assume positive interest rates in time value analyses, the present value of a three-year annuity will always be less than the future value of a single lump sum, if the sum of the annuity payments equals the original lump sum investment.

Accepted Answer

If the interest rate is positive, the present value of the annuity will always be less than the future value of the single lump sum investment, regardless of the duration of the payments.

Question 7

The greater the number of compounding periods within a year, the greater the future value of a lump sum invested initially, and the greater the present value of a given lump sum to be received at maturity.

Accepted Answer

The greater number of compounding periods within a year increases the future value of a lump sum invested initially due to more frequent application of interest, but it decreases the present value of a given lump sum to be received at maturity because more compounding periods mean a higher effective discount rate is applied to the future value.

Question 8

Cash flow time lines are used primarily for decisions involving paying off debt or investing in financial securities.
They cannot be used when making decisions about investments in physical assets.

Accepted Answer

Cash flow time lines can be used for making decisions about investments in physical assets, such as determining the payback period or net present value of the investment.

Question 9

Suppose an investor can earn a steady 5% annually with investment A, while investment B will yield a constant 12% annually.Within 11 years time, the compounded value of investment B will be more than twice the compounded value of investment A (ignore risk).

Accepted Answer

Using the compound interest formula A = P(1+r/n)^(nt), where A is the compounded value, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years, we can solve for the time it takes for investment B to be more than twice that of investment A:

For Investment A:
A = P(1+r/n)^(nt)
A = P(1+0.05/1)^(1*11)
A = P(1.05)^11

For Investment B:
A = P(1+r/n)^(nt)
A = P(1+0.12/1)^(1*t)
A = P(1.12)^t

To find when Investment B is more than twice Investment A, we set the equations equal to each other and solve for t:

2(P(1.05)^11) = P(1.12)^t
2(1.05)^11 = (1.12)^t
t ≈ 5.66 years

Since it only takes 5.66 years for Investment B to be more than twice that of Investment A, and we are looking at a time period of 11 years, it is true that Investment B will be more than twice the compounded value of Investment A within 11 years time.

Question 10

The coupon rate is the rate of return you could earn on alternative investments of similar risk.

Accepted Answer

The coupon rate is the annual interest rate paid by the bond issuer on the bond's face value, not the rate of return on alternative investments.

Question 11

Solving for the interest rate associated with a stream of uneven cash flows, without the use of a calculator, usually involves a trial and error process.

Accepted Answer

This is because there is no general formula to directly solve for the interest rate in such cases, and so an iterative process involving multiple guesses and calculations is often required.

Question 12

One of the potential benefits of investing early for retirement is that an investor can receive greater benefits from the compounding of interest.

Accepted Answer

When an investor starts investing early for retirement, their money has more time to grow through compounding interest. Compounding interest allows the investor to earn interest not only on their initial investment but also on the interest earned from that investment. Over time, this can lead to significant growth in the investor's retirement savings.

Question 13

The effective annual rate is less than the simple rate when we have monthly compounding.

Accepted Answer

The effective annual rate is greater than the simple rate when there is monthly compounding because it accounts for the effects of compounding within the year.

Question 14

An annuity is a series of equal payments made at fixed equal-length intervals for a specified number of periods.

Accepted Answer

An annuity is indeed a series of equal payments made at fixed equal-length intervals for a specified number of periods.

Question 15

Given some amount to be received several years in the future, if the interest rate increases, the present value of the future amount will
A)Be higher.
B)Be lower.
C)Stay the same.
D)Cannot tell.
E)Be variable.

Accepted Answer

When the interest rate increases, the present value of the future amount will be lower because the discount rate used to calculate the present value increases, making the future amount worth less in today's dollars.

Question 16

A perpetuity is an annuity with perpetual payments.

Accepted Answer

A perpetuity is a type of annuity where the payments continue indefinitely, which makes it different from a typical annuity that has a fixed period of payments.

Question 17

An amortized loan is a loan that requires equal payments over its life; its payments include both interest and repayment of the debt.

Accepted Answer

An amortized loan is structured so that the payments made over the life of the loan are equal and include both interest and repayment of the debt. This is different from other types of loans, such as interest-only loans, which only require payments toward the interest and do not reduce the principal balance of the loan.

Question 18

Of all the techniques used in finance, the least important is the concept of the time value of money.

Accepted Answer

The concept of the time value of money is considered very important in finance because it helps individuals and companies make informed decisions regarding investments, budgeting, and financial planning. It helps to understand that a dollar received today is worth more than a dollar received in the future due to the impact of inflation and interest rates. Therefore, it is crucial to consider the time value of money while making financial decisions.

Question 19

The difference between an ordinary annuity and an annuity due is that each of the payments of the annuity due earns interest for one additional year (period).

Accepted Answer

An annuity due is similar to an ordinary annuity except that each payment of the annuity due earns interest for one additional year, making it slightly more valuable than an ordinary annuity with the same terms.

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?
A)The discount rate decreases.
B)The cash flows are extended over a longer period of time, but the total amount of the cash flows remains the same.
C)The discount rate increases.
D)Answers b and c above.
E)Answers a and b above.

Accepted Answer

When the discount rate decreases, the present value of future cash flows increases. This means that the project becomes more profitable and appealing. Option B only extends the time period, but does not change the total amount of cash flows, so it does not have an impact on present value. Option C would decrease the present value of the cash flows and make the project less profitable. Therefore, the best choice is A.

Quiz 4: Time Value of Money