Question 1

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, such as quarterly or semi-annually. However, it may require adjustments to accurately reflect the timing and magnitude of the cash flows.

Question 2

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 according to the principles of time value of money. A positive discount or interest rate means that money is worth more in the present than in the future, so future payments must be discounted to their present value. This results in the present value being lower than the future value of the same series of payments.

Question 3

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 4

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 5

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 6

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, it means that interest is added to the account balance every three months. This results in an effective annual rate (EAR) that is higher than the nominal rate, as the interest is being compounded more frequently than once per year. Therefore, the effective annual rate will exceed the nominal rate.

Question 7

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

Accepted Answer

Starting to invest early for retirement maximizes the benefits of compound interest, as the money has more time to grow and compound.

Question 8

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 means that it can earn interest over time. Therefore, the future value of a given sum can exceed its present value if it earns interest. However, this statement disregards risk, which can affect the actual return on an investment.

Question 9

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 frequency of interest being added to the investment, leading to a higher future value. Additionally, discounting at a higher frequency reduces the present value.

Question 10

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 is added to the account four times a year. This means that the interest earned on each quarter includes interest on the interest from the previous quarters. This compounding effect results in a higher effective annual rate compared to the nominal rate, which is the annual rate without considering the effects of compounding.

Question 11

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 in which payments occur at the beginning of the periods as well as at the end. It just requires adjusting the timing of the first payment and the time intervals between subsequent payments on the timeline.

Question 12

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

Accepted Answer

The earlier someone starts investing for retirement, the more time their money has to benefit from compound interest, which can significantly increase their retirement savings.

Question 13

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 14

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 cash flows regardless of their frequency, and it is common to construct time lines for cash flows that occur quarterly.

Question 15

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 possible to have a combination of annuity payments and uneven amounts on a time line. An annuity is a series of payments of equal amounts made at regular intervals, while uneven amounts may be one-time payments or irregular payments made at different intervals.

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

This statement is true. Time lines are a visual representation of annuity payments and can be constructed for both beginning-of-period and end-of-period payments.

Question 17

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 points in time. Including situations where some cash flows occur annually and others occur quarterly. The time line would simply be divided into quarterly intervals to accurately reflect the timing of the cash flows.

Question 18

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 19

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

Accepted Answer

A time line can still show the timing and amount of cash flows, even if they do not occur annually. It can show the periods of time between when cash flows occur and allow for the calculation of the time value of money.

Question 20

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, with an initial investment of $1,000, we can calculate the compounded value after 11 years for Security A as $1,000 x (1 + 0.05)^11 = $1,697.63, and for Security B as $1,000 x (1 + 0.12)^11 = $3,105.85. As $3,105.85 is more than twice $1,697.63, the statement is true.

Quiz 5: The Value of Money