Question 1

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

Accepted Answer

If money has time value, it is possible for the future value of a given sum to exceed its present value through the application of compound interest.

Question 2

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 3

Some of the cash flows shown on a time line can be in the form of annuity payments while others can be uneven amounts.

Accepted Answer

This is true. An annuity is a series of equal payments made at regular intervals, while uneven payments are those that vary in size and timing. Both types of cash flows can be shown on a time line.

Question 4

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 5

Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods.

Accepted Answer

This is true. When constructing a timeline for an annuity, it is important to specify whether payments occur at the beginning or end of each period. This information affects how the timeline is drawn and how calculations are made.

Question 6

Time lines can be constructed in situations where some of the cash flows occur annually but others occur quarterly.

Accepted Answer

Time lines can be constructed for any situation where there are cash flows, regardless of the frequency of those cash flows. Cash flows that occur annually and those that occur quarterly can both be incorporated into a time line.

Question 7

Some of the cash flows shown on a time line can be in the form of annuity payments but none can be uneven amounts.

Accepted Answer

Cash flows shown on a timeline can include both annuity payments (which are equal amounts occurring at regular intervals) and uneven amounts, reflecting the variability in cash flows that can occur in real-world scenarios.

Question 8

Starting to invest early for retirement increases the benefits of compound interest.

Accepted Answer

Investing early allows for more time for compound interest to accrue, resulting in greater long-term benefits.

Question 9

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

Accepted Answer

This is because a positive discount rate reflects the time value of money, which accounts for the opportunity cost of having to wait to receive the payments. As time goes on, the present value of the payments decreases while the future value increases, making the future value greater than the present value.

Question 10

Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly.

Accepted Answer

Time lines can be constructed for any type of cash flow, regardless of the frequency of occurrence. The time line would simply have a shorter interval for the more frequent cash flows (e.g. quarterly intervals for quarterly cash flows, annual intervals for annual cash flows).

Question 11

A time line is not meaningful unless all cash flows occur annually.

Accepted Answer

A time line can still be meaningful even if cash flows occur at different frequencies, such as monthly or quarterly, as long as the time line includes all relevant cash flows and adjusts for the frequency of those cash flows.

Question 12

A time line is meaningful even if all cash flows do not occur annually.

Accepted Answer

A time line is a visual representation of cash flows over time, and it can show cash flows occurring at any interval (monthly, quarterly, biannually, etc.), not just annually. As long as the time line accurately represents the timing and amount of cash flows, it is meaningful.

Question 13

Suppose Randy Jones plans to invest $1,000. He can earn an effective annual rate of 5% on Security A, while Security B has an effective annual rate of 12%. After 11 years, the compounded value of Security B should be somewhat less than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.)

Accepted Answer

Given the effective annual rates and the compounding period of 11 years, the compounded value of Security B will be significantly more than twice the compounded value of Security A due to the higher interest rate of Security B (12% vs. 5%). The formula for compound interest $A = P(1 + r)^n$ shows that a higher rate over the same period results in exponentially greater returns.

Question 14

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

Accepted Answer

Compounding quarterly means that the interest is added to the account balance every three months. This results in more frequent compounding than if it were compounded annually, which leads to a higher effective annual rate.

Question 15

Suppose Sally Smith plans to invest $1,000. She can earn an effective annual rate of 5% on Security A, while Security B has an effective annual rate of 12%. After 11 years, the compounded value of Security B should be more than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.)

Accepted Answer

Using the formula for compound interest, we can determine the compounded value of each security after 11 years:

For Security A:
Compounded value = $1,000 * (1 + 0.05)^11 = $1,629.64

For Security B:
Compounded value = $1,000 * (1 + 0.12)^11 = $3,435.75

As we can see, the compounded value of Security B is indeed more than twice that of Security A. Therefore, the statement is true.

Question 16

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 17

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

Accepted Answer

Compounding quarterly actually results in a higher effective annual rate compared to compounding annually. Therefore, the effective annual rate will exceed the nominal rate.

Question 18

Starting to invest early for retirement reduces the benefits of compound interest.

Accepted Answer

Starting to invest early for retirement actually increases the benefits of compound interest. The earlier you start, the longer your money has to grow and compound, resulting in potentially significant returns over time.

Question 19

Time lines cannot be constructed for annuities unless all the payments occur at the end of the periods.

Accepted Answer

Time lines can be constructed for annuities with payments made at the beginning of the periods as well as at the end. The construction of the time line may differ slightly depending on when the payments are made, but it is still possible to represent an annuity with payments made at the beginning of the periods.

Question 20

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 smaller the present value of a given lump sum to be received at some future date.

Accepted Answer

This is because compounding more frequently increases the effective interest rate, leading to higher future values, but decreases the present value due to time value of money calculations.

Quiz 5: Time Value of Money