Question 1

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

Accepted Answer

If a bank compounds savings accounts quarterly, the effective annual rate will be greater than the nominal rate. This is because compounding more frequently leads to higher interest earnings over time.

Question 2

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 that occur at any regular frequency, including both annual and quarterly cash flows.

Question 3

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

Accepted Answer

Time lines can easily accommodate cash flows that occur at different intervals of time, including annually and quarterly.

Question 4

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 find the compounded value of each security:
For Security A:

$1000(1+0.05)^{11} = $1,677.10

For Security B:

$1000(1+0.12)^{11} = $3,370.24

Since we want the compounded value of Security B to be more than twice that of Security A:

2($1000(1+0.05)^{11})<$1000(1+0.12)^{11}

$3,354.19<$3,370.24

Therefore, Security B's compounded value should be greater than twice that of Security A after 11 years.

Question 5

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

Accepted Answer

A time line can still have meaningful interpretation despite cash flows occurring at different time intervals. However, for ease of calculation, it is usually assumed that all cash flows occur annually.

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

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 8

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 regardless of whether the payments occur at the beginning or end of the periods, as long as the timing is consistent.

Question 9

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

Accepted Answer

A time line can show cash flows that occur at different intervals, such as monthly or quarterly, and still provide a clear representation of the timing and magnitude of each cash flow. The time line can be adjusted and labeled accordingly to accurately depict the cash flow schedule.

Question 10

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 11

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, allowing for greater potential growth and a higher final investment value.

Question 12

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 true according to the time value of money concept. The discount rate represents the opportunity cost of investing money in the present instead of using it for other purposes. Therefore, when the discount rate is positive, the future value of a series of payments will always be higher than their present value because the discount rate discount the present value to a lower amount in the future.

Question 13

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 can show the payments of annuities occurring at the beginning or end of the periods, and the choice of when the payments occur can affect the calculation of the annuity's present value or future value.

Question 14

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

The statement is incorrect. If money has time value, then with the right interest rate, the future value of a given sum can indeed exceed its present value. This is the basis for investing and earning interest or returns on investments.

Question 15

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 amount, resulting in a higher overall balance that earns more interest. This leads to a higher effective annual rate than the nominal rate.

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 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, the investment has more opportunities to earn interest, leading to a larger future value. Additionally, the present value decreases with more compounding periods because the value of money decreases over time due to inflation and the opportunity cost of not investing the money immediately.

Question 17

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 cash flow time line. An annuity is a series of equal payments made at regular intervals, while uneven amounts refer to payments that vary in amounts and/or timing.

Question 18

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 19

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

Accepted Answer

By starting to invest early, there is more time for the interest on investments to compound, leading to greater returns in the long run.

Question 20

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.

Quiz 5: Time Value of Money