Question 1

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 with any time interval, including annual and quarterly cash flows.

Question 2

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

While the first statement is true as more frequent compounding periods increase the future value of an investment, the second statement is false because more frequent compounding reduces the present value of a future lump sum, as the discount rate applied per period is smaller.

Question 3

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

Accepted Answer

Cash flows could occur monthly, quarterly, or bi-annually, which would require the use of appropriate compounding or discounting techniques to create a meaningful time line.

Question 4

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

Some of the cash flows on a time line can indeed be in the form of annuity payments (which are equal payments made at regular intervals), but cash flows can also be uneven amounts, representing irregular payments or receipts.

Question 5

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 type of cash flow stream where the payments increase at a constant rate over a specified period of time. This is different from a regular annuity where the payments remain the same.

Question 6

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 7

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

Accepted Answer

A time line allows for the visualization of the timing and amounts of cash flows, regardless of whether they occur annually or not. The time line can include cash flows that occur on a monthly, quarterly, or even a daily basis, and still be meaningful in helping to understand the cash flow patterns and needs of a project or investment.

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 because your money has more time to grow and accumulate returns.

Question 9

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

Accepted Answer

Compounding quarterly (4 times a year) means that interest is earned on the previous interest earned every 3 months. This results in a higher effective annual rate than the nominal rate, which is the interest rate stated without the effect of compounding.

Question 10

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 false. The future value of a given sum can exceed its present value if it earns interest or experiences inflation over time. Therefore, the statement "if money has time value, it is impossible for the future value of a given sum to exceed its present value" is incorrect.

Question 11

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

Accepted Answer

When you start investing early for retirement, you give your money more time to grow through compound interest. This means that not only are you earning interest on your original investment, but you are also earning interest on the interest you have already earned. Over time, this can lead to significant growth and higher retirement savings.

Question 12

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 13

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 compounding periods allow for more interest to be earned on the initial investment, increasing the future value. Additionally, more compounding periods decrease the present value of a future lump sum because the interest earned on the investment reduces the amount needed to be invested at Time 0 to reach the same future value.

Question 14

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 statement is referring to the concept of time value of money, which states that money today is worth more than the same amount of money in the future. Therefore, a positive discount or interest rate will increase the present value of future payments, making the future value of the same series exceed the present value.

Question 15

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 both types of annuities, where payments occur at the beginning or the end of the periods.

Question 16

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 for cash flows to be in the form of annuity payments or uneven amounts.

Question 17

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 in situations where cash flows occur at different frequencies. The time line can be adjusted to show the quarterly cash flows in between the annual cash flows.

Question 18

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 nominal rate is divided by four to calculate the quarterly rate, which is then applied four times a year. This results in the effective annual rate being slightly higher than the nominal rate.

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 both end-of-period payments and beginning-of-period payments. However, for simplicity, most textbooks and finance calculators assume end-of-period payments unless explicitly stated otherwise.

Question 20

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 given amount of money is worth more now than the same amount in the future due to its potential earning capacity. Therefore, the present value of a sum will always be less than its future value when not considering risk.

Quiz 4: Time Value of Money