Question 1

Which of the following statements best describes time lines?

Accepted Answer

Time lines are an important tool for visualizing cash flows and making calculations easier. They can be used for any cash flow scenario, regardless of the frequency of payments or whether they are annuities or not. It is not necessary for all cash flows to occur annually, and time lines can be constructed for both ordinary annuities (end-of-period payments) and annuities due (beginning-of-period payments).

Question 2

Midway through the life of an amortized loan, the percentage of the payment that represents interest is equal to the percentage that represents principal repayment. This is true regardless of the original life of the loan.

Accepted Answer

In an amortized loan, the interest portion of the payment decreases over time, while the principal portion increases. This means that midway through the life of the loan, the payment is not equally divided between interest and principal; rather, more of the payment is applied towards the principal than at the beginning of the loan.

Question 3

Which of the following statements is correct?

Accepted Answer

To solve for I, one needs to find the value of I that makes the PV of all positive cash flows equal to the absolute value of the PV of all negative cash flows. This is a trial-and-error procedure that can be simplified with financial calculators or computers but is difficult otherwise. Therefore, option B is the correct statement.

Question 4

When a loan is amortized, a relatively high percentage of the payment goes to reduce the outstanding principal in the early years, and the principal repayment's percentage declines in the loan's later years.

Accepted Answer

In an amortized loan, the early payments consist of a higher percentage of interest and a lower percentage of principal reduction. As the loan matures, the portion of the payment reducing the principal increases, while the interest portion decreases.

Question 5

Which of the following bank accounts has the highest effective annual return?

Accepted Answer

The account that pays 8% nominal interest with daily (365-day) compounding has the highest effective annual return. This is because daily compounding results in more frequent compounding periods, which increases the effective annual return.

Question 6

The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the greater the present value of a given lump sum to be
received at some future date.

Accepted Answer

The greater number of compounding periods increases the future value of a lump sum investment due to more frequent application of interest, but it decreases the present value of a future lump sum because more compounding periods mean a higher effective discount rate is applied, reducing the present value.

Question 7

The present value of a future sum decreases as either the discount rate or the number of periods per year increases.

Accepted Answer

This is true as increasing the discount rate or the number of periods per year increases the amount of interest earned or compounded, thus reducing the present value of a future sum.

Question 8

Your bank account pays a 6% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is correct?

Accepted Answer

The periodic rate of interest is calculated by taking the nominal rate and dividing it by the number of compounding periods per year: 6%/4 = 1.5%. The effective rate of interest takes into account the compounding effect and is calculated using the formula (1 + r/n)^n - 1, where r is the nominal rate and n is the number of compounding periods per year. So, the effective rate of interest in this case is (1 + 6%/4)^4 - 1 = 6.136%, which is greater than 6%. Therefore, the correct statement is: The periodic rate of interest is 1.5% and the effective rate of interest is greater than 6%.

Question 9

Disregarding risk, if money has time value, it is impossible for the present value of a given sum to exceed its future value.

Accepted Answer

The time value of money principle states that a dollar today is worth more than a dollar in the future due to its potential earning capacity. Therefore, the present value of a given sum, when considering the time value of money, will always be less than its future value.

Question 10

If a bank compounds savings accounts quarterly, the nominal rate will exceed the effective annual rate.

Accepted Answer

If a bank compounds savings accounts quarterly, the effective annual rate will be higher than the nominal rate. This is because compounding more frequently increases the effective rate.

Question 11

As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal to or greater than the nominal rate on the deposit (or loan).

Accepted Answer

Compounding takes into account the interest earned on both the principal amount and any accumulated interest. This leads to a higher effective annual rate than the nominal rate.

Question 12

Which of the following statements is INCORRECT?

Accepted Answer

A time line can still be constructed for cash flows that occur quarterly or at other intervals, but it may require adjusting the time axis on the graph. Therefore, statement A is incorrect as it implies that time lines are only meaningful for annual cash flows.

Question 13

Suppose an investor plans to invest a given sum of money. She can earn an effective annual rate of 5% on Security A, while Security B will provide an effective annual rate of 12%. Within 11 years' time, the compounded value of Security B will be more than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.)

Accepted Answer

Using the compound interest formula and solving for the given conditions, we get:

For Security A:
Compounded value = P(1 + r/n)^(nt)
Compounded value = P(1 + 0.05/1)^(1*11)
Compounded value = 1.628P

For Security B:
Compounded value = P(1 + r/n)^(nt)
Compounded value = P(1 + 0.12/1)^(1*11)
Compounded value = 4.317P

Since the compounded value of Security B is more than twice the compounded value of Security A (4.317P > 2*1.628P), the statement is true.

Question 14

All other factors held constant, the present value of a given annual annuity decreases as the number of discounting periods per year increases.

Accepted Answer

This is because the more discounting periods there are per year, the more times the interest rate is applied to the cash flows, causing the present value to decrease.

Question 15

You are analyzing the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would lower the calculated value of the investment?

Accepted Answer

If the discount rate increases, the present value of future cash flows decreases, which lowers the calculated value of the investment.

Question 16

If the discount (or interest) rate is positive, the present value of an expected series of payments will always exceed the future value of the same series.

Accepted Answer

The present value of an expected series of payments will be less than the future value of the same series if the discount (or interest) rate is positive, because the value of money decreases over time when the rate is positive.

Question 17

One potential benefit from starting to invest early for retirement is that the investor can expect greater benefits from the compounding of interest.

Accepted Answer

When an investor starts saving for retirement early, their investment will have more time to grow and generate interest. Over time, the interest earned on the investment can also earn interest, which is known as compounding interest. This can result in significant returns over a long period of time.

Question 18

Which of the following statements best describes annuities?

Accepted Answer

An annuity is a series of equal cash flows that occur at regular intervals, such as once a year or once a month. The cash flows can occur at either the beginning (ordinary annuity) or end (annuity due) of each period. Therefore, statement A and C are incorrect. Statement B is also incorrect because the cash flows must be equal to be considered an annuity.

Question 19

If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by multiplying the periodic rate by the number of periods per year.

Accepted Answer

This is correct. The formula for finding the nominal annual rate is: Nominal Annual Rate = Periodic Rate x Number of Periods per Year. Therefore, if we are given a monthly interest rate, we can multiply it by 12 (the number of months in a year) to find the annual rate.

Question 20

The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan's life, the greater the percentage of the payment that will be a repayment of principal.

Accepted Answer

This is the basic principle of amortization, where a larger portion of the payment goes towards principal repayment as the loan nears maturity.

Quiz 4: Time Value of Money