Question 1

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

Accepted Answer

Compound interest is the interest earned not only on the initial investment but also on the interest accrued over time. By investing early, there is more time for the interest to compound, resulting in higher returns on the investment over time.

Question 2

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. However, it may require additional calculations or adjustments to properly account for the timing of cash flows.

Question 3

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 different frequencies, including annually and quarterly. The time line would simply depict each cash flow at its respective time point, regardless of whether it occurs annually or quarterly.

Question 4

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

Accepted Answer

This statement is false. Starting to invest early for retirement actually maximizes the benefits of compound interest, as the interest earned on investments can accumulate over a longer period of time, leading to a greater return on investment.

Question 5

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

Accepted Answer

A time line can still be used to represent cash flows that occur at irregular intervals, such as quarterly or semi-annually. The time scale on the timeline can be adjusted accordingly.

Question 6

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 7

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 mean that interest is being added more frequently, leading to a higher overall amount in the future. Additionally, the smaller present value is due to the fact that more compounding periods mean that the discount rate is applied more frequently, leading to a lower present value.

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, the future value of a given sum can exceed its present value, as long as the interest rate or rate of return is high enough to compensate for the time value of money.

Question 9

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 nominal rate and effective annual rate will be the same. However, if the savings account is compounded more frequently (such as monthly or daily), the effective annual rate will be higher than the nominal rate.

Question 10

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 11

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

Accepted Answer

Compounding quarterly means that the interest earned is added to the account balance every three months. This leads to more frequent compounding and a higher effective annual rate compared to simple annual interest.

Question 12

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. Annuity payments are a series of equal payments made at equal intervals, while other cash flows can be uneven amounts.

Question 13

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 14

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 15

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 periodicity, including annually and quarterly.

Question 16

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 17

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 payments occur at the end or beginning of the periods. However, the timing of the payments will impact the calculations of certain variables such as present value, future value, and payment amount.

Question 18

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 because the discount rate takes into account the time value of money, meaning that money received in the future is worth less than money received today due to factors such as inflation and the opportunity cost of not being able to invest the money elsewhere. Therefore, the discount rate effectively reduces the value of future payments, making the present value of the series lower than the future value.

Question 19

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, we can set up the following equation:

$1,000(1+0.05)^{11} < 2 \cdot 1,000(1+0.12)^{11}$

Simplifying this equation, we get:

$1.05^{11} < 2 \cdot 1.12^{11}$

Evaluating the left and right hand side of this inequality, we get:

1.79585 < 3.17808

Since the right hand side is greater than the left hand side, Security B will have a compounded value more than twice that of Security A after 11 years. Therefore, the answer is true.

Question 20

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 be constructed for annuities where the payments occur at the beginning or the end of the periods. The time line will be adjusted accordingly, with payments shown at the beginning or end of each period.

Quiz 5: Time Value of Money