Question 1

As the number of periods increases, present value increases.

Accepted Answer

As the number of periods increases, the present value actually decreases. This is because the value of money decreases over time due to inflation or the opportunity cost of investing elsewhere, therefore the present value of a future sum of money decreases the further out it is in time.

Question 2

As the interest rate increases, present value decreases.

Accepted Answer

This is because as the interest rate increases, the cost of borrowing or earning money in the future increases, making the value of money in the present worth less. Therefore, the present value of a future cash flow decreases as the interest rate increases.

Question 3

The effective annual rate is determined by multiplying the interest rate charged per period by the number of periods in a year.

Accepted Answer

The effective annual rate is calculated by taking into account the effect of compounding over the year, not simply by multiplying the interest rate per period by the number of periods in a year.

Question 4

At a zero interest rate, the present value of $1 remains at $1 and is not affected by time.

Accepted Answer

At a zero interest rate, there is no discounting of future cash flows, so the present value of $1 remains constant regardless of time.

Question 5

An annuity is a series of equal payments that occur over a number of time periods.

Accepted Answer

An annuity is a series of equal payments that occur over a specific number of time periods.

Question 6

Simple interest is interest earned on the investment's principal and subsequently-earned interest.

Accepted Answer

Simple interest is interest earned only on the original principal amount, not on the interest accrued over time.

Question 7

Discounting is an arithmetic process whereby a future value sum decreases at a compounding interest rate over time to reach a present value.

Accepted Answer

This is an accurate definition of discounting, where the future value decreases as it is discounted back to its present value using a compounding interest rate.

Question 8

The method of calculating the annual percentage rate (APR) is set by law.

Accepted Answer

The Truth in Lending Act requires lenders to disclose the APR and sets forth specific requirements for how it must be calculated.

Question 9

Compound interest is interest earned on interest in addition to interest earned on the principal.

Accepted Answer

Compound interest is calculated based on the principal and any interest earned that has been added to the principal, so interest is earned on the interest as well as the principal.

Question 10

An amortized loan is repaid in equal payments over a specified time period.

Accepted Answer

An amortized loan is a loan that is repaid in equal payments over a specified time period, typically with the payment amount consisting of a portion of both the principal and interest.

Question 11

For a given discount rate, an ordinary annuity and an annuity due have the same present value.

Accepted Answer

An ordinary annuity and an annuity due have different present values for the same cash flows and discount rate because the payments of an annuity due occur at the beginning of each period, while the payments of an ordinary annuity occur at the end of each period. This difference in timing affects the calculation of present value.

Question 12

For the same annual percentage rate, more frequent compounding increases the future value of an investor's funds more quickly.

Accepted Answer

This is true because compounding more frequently means that the interest earned during each compounding period is added to the principal, allowing for greater growth over time.

Question 13

If the compound inflation rate were greater than the compound interest rate, future purchasing power on our savings would fall.

Accepted Answer

If the compound inflation rate is higher than the compound interest rate, the value of our savings will decrease over time due to the rising prices of goods and services. This means that our purchasing power will also fall.

Question 14

The Rule of 72 is an estimate of how long it would take to double a sum of money at a given interest rate.

Accepted Answer

The Rule of 72 states that you can divide the interest rate into 72 to estimate how many years it will take for an investment to double in value. For example, if you have an interest rate of 6%, it would take approximately 12 years to double your money (72 divided by 6 equals 12).

Question 15

The annual percentage rate is the true opportunity cost measure of the interest rate.

Accepted Answer

The annual percentage rate (APR) includes not only the interest rate but also other charges or fees to reflect the total cost of a loan, making it different from the true interest rate which does not account for additional fees.

Question 16

An ordinary annuity exists when the equal payments occur at the beginning of each time period.

Accepted Answer

An ordinary annuity exists when the equal payments occur at the end of each time period.

Question 17

A fixed-rate mortgage is an example of an annuity.

Accepted Answer

A fixed-rate mortgage involves making consistent payments of the same amount over a set period of time, making it an annuity.

Question 18

Money has a time value so long as interest is earned by saving or investing money.

Accepted Answer

Money has the ability to earn interest through saving or investing. This means that money today is worth more than the same amount of money in the future. Therefore, money has a time value.

Question 19

An annuity due may also be referred to as a deferred annuity.

Accepted Answer

An annuity due is not the same as a deferred annuity. An annuity due is an annuity where payments are made at the beginning of each period, while a deferred annuity is an annuity where payments are postponed until a specified future date.

Question 20

When the annual interest rate stays the same, more frequent interest compounding helps savers earn more interest over the course of the year.

Accepted Answer

This is true because with more frequent compounding, interest is being added to the account more frequently and therefore the balance grows faster, resulting in more interest earned over time.

Quiz 9: Time Value of Money