Question 1

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 at different intervals such as annually and quarterly. The cash flows at different intervals would simply be placed on different parts of the time line, such as marking the annual cash flows on the main horizontal axis and marking the quarterly cash flows on a smaller vertical axis.

Question 2

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

Accepted Answer

Compounding quarterly (4 times a year) increases the effective annual rate because each quarter, the interest earned is added to the principal, which then earns interest in the next quarter. This results in a higher overall interest earned compared to simple interest calculations. Therefore, the effective annual rate will exceed the nominal rate.

Question 3

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 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 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 5

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

Accepted Answer

Compounding quarterly will result in a higher effective annual rate, as compared to the nominal rate. This is because the interest is being compounded more frequently, leading to a higher overall return.

Question 6

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 intervals (e.g. quarterly, monthly, etc.). However, the time line should reflect the exact timing of the cash flows for accurate analysis.

Question 7

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 true because a positive discount (or interest) rate accounts for the time value of money and the fact that money today is worth more than the same amount of money in the future. As a result, the future value of an expected series of payments will always be higher than the present value of the same series, assuming a positive discount (or interest) rate.

Question 8

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, as the interest earned on your investments will also earn interest over time. This compounding effect results in a greater potential for growth and higher returns in the long run.

Question 9

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 10

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 11

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, as some cash flows may occur at regular intervals and be in the form of annuity payments, while others may be one-time or irregular amounts.

Question 12

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

Accepted Answer

A time line can include cash flows that occur at different intervals, such as quarterly or semi-annually. The time line allows for visualization and analysis of the timing and amount of cash flows.

Question 13

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 type of cash flow, regardless of whether they occur annually, quarterly, monthly, or even daily. The time line simply needs to be adjusted to show the appropriate intervals between cash flows.

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 occurring at the beginning or end of the periods. However, the timing of the payments can affect the calculation of the present value, future value, and other measures of the annuity.

Question 15

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, but this would only happen if the growth rate of the investment exceeds the discount rate used to calculate the present value. However, this statement disregards risk, which is an important factor in investment decisions.

Question 16

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

Accepted Answer

Time lines can be constructed for annuities regardless of whether payments occur at the beginning or end of the periods. However, the timing of the payments will affect the calculations used to determine the present value or future value of the annuity.

Question 17

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 each subsequent payment increases by a constant amount or rate for a certain number of periods, resulting in a growing cash flow stream.

Question 18

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

Accepted Answer

By starting to invest early for retirement, individuals have more time for their money to grow through compound interest, which can significantly increase their savings over time.

Question 19

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 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 more frequent compounding means the interest earned on an investment is being reinvested more often, leading to a higher overall return. On the other hand, more frequent compounding also means that the discount rate used to calculate present value increases, resulting in a smaller present value for a given lump sum.

Quiz 4: Time Value of Money