Question 1

A "growing annuity" is a cash flow stream that grows at a constant rate for a specified number of periods.

Accepted Answer

A growing annuity is a cash flow stream where the payments increase by a constant rate for a specified number of periods.

Question 2

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

Accepted Answer

When a bank compounds savings accounts quarterly, the interest earned in each quarter is added to the principal, resulting in more interest being earned in subsequent quarters. This results in a higher effective annual rate than the nominal rate.

Question 3

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 4

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 with more compounding periods, there is more frequent interest earning, resulting in a larger future value over time. Additionally, a smaller present value is needed to reach the same future value due to the impact of compounding.

Question 5

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 situations where cash flows occur annually or quarterly or any other time period. The time line simply needs to appropriately represent the time intervals between cash flows.

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

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

This statement is incorrect. If money earns interest over time, the future value of a given sum can exceed its present value.

Question 8

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

It is common for cash flows to include a combination of annuity payments as well as uneven amounts. Annuity payments are simply a series of equal cash flows received or paid at equal intervals, while uneven amounts refer to cash flows that vary over time.

Question 9

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. Time lines can be constructed for annuities with payments occurring at the beginning or end of periods.

Question 10

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

Accepted Answer

Starting to invest early actually increases the benefits of compound interest as the invested funds have more time to grow and earn returns over a longer period of time. Therefore, it is recommended to start investing as early as possible for retirement.

Question 11

A "growing annuity" is any cash flow stream that grows over time.

Accepted Answer

The answer of A "growing annuity" is any cash flow...

Question 12

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 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 interest is compounded per year, and t is the number of years:

For Security A, A = 1000(1+0.05/1)^(1*11) = $1,629.17
For Security B, A = 1000(1+0.12/1)^(1*11) = $3,105.85

Since the compounded value of Security B should be more than twice the compounded value of Security A after 11 years, we can set up the following inequality:

$3,105.85 > 2($1,629.17)
$3,105.85 > $3,258.34

This inequality is true, so the statement is true.

Question 13

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 14

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 15

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

Accepted Answer

When a bank compounds savings accounts quarterly, the effective annual rate will be higher than the nominal rate. This is because compounding more frequently results in earning interest on interest, which increases the effective annual rate.

Question 16

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 cash flows occur at different intervals, including both annual and quarterly. The time line will simply show the specific timing and frequency of each cash flow.

Question 17

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

Accepted Answer

When you start investing early, you have more time for your money to grow with the help of compound interest. As a result, even a small amount of money invested regularly can turn into a significant sum over time.

Question 18

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

Accepted Answer

A time line can be used to illustrate cash flows that occur at different intervals, such as monthly, quarterly or bi-annually. The time line simply needs to be labeled and scaled appropriately to represent the timing of the cash flows.

Question 19

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 do not occur annually, although it may require additional analysis and adjustments such as discounting or compounding.

Question 20

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.

Quiz 4: Time Value of Money