Question 1

To evaluate or compare investment proposals,we must adjust the value of all cash flows to a common date.

Accepted Answer

This is true because comparing investment proposals that require different initial cash flows, timing, and duration would require the use of a common evaluation metric. The process of adjusting all cash flows to a common date is known as discounting, and it is an essential component of discounted cash flow analysis, which is used to evaluate investment opportunities.

Question 2

If the interest rate is positive,a six-year ordinary annuity of $500 per year must have a present value over $3,000.

Accepted Answer

The present value of an annuity is calculated by discounting each payment back to its present value at the given interest rate. If the interest rate is positive, the present value of each $500 payment will be less than $500, making the total present value of all payments less than $3,000.

Question 3

If the interest rate is positive,then the present value of an annuity due will be less than the present value of an ordinary annuity.

Accepted Answer

The present value of an annuity due is greater than the present value of an ordinary annuity because payments for an annuity due are made at the beginning of each period, allowing each payment to accrue interest for an additional period compared to an ordinary annuity, where payments are made at the end of each period.

Question 4

John has to pay $1,000 per month for his mortgage for another 5 years,but he is considering paying the mortgage off in one lump sum.John cannot calculate the present value of the payments using the annuity formulas because his payments are monthly and not once per year.

Accepted Answer

The annuity formulas can be adjusted to account for different payment periods, including monthly payments, by modifying the interest rate and the number of periods accordingly.

Question 5

The future value of a 10-year ordinary annuity is twice as much as the future value of an otherwise identical 5-year annuity.

Accepted Answer

The future value of a 10-year ordinary annuity is not necessarily twice as much as that of a 5-year annuity because the future value also depends on the interest rate and the frequency of compounding, not just the duration.

Question 6

An example of an annuity is the interest received from bonds.

Accepted Answer

An annuity is a financial product that provides a fixed stream of payments at regular intervals, typically for retirement or investment purposes. The interest received from bonds is a type of annuity, as it provides a fixed stream of payments (interest) at regular intervals (usually annually or semi-annually) until the bond matures.

Question 7

If the future value of annuity A is greater than the future value of annuity B,then the present value of annuity A must also be greater than the present value of annuity B.

Accepted Answer

This statement is true because the present value of an annuity is directly proportional to its future value. If one annuity has a higher future value than another annuity, it must also have a higher present value.

Question 8

When repaying an amortized loan,the interest payments increase over time due to the compounding process.

Accepted Answer

The interest payments decrease over time as the principal balance decreases and less interest accrues on the remaining balance.

Question 9

The present value of a deferred annuity (e.g.,an annuity that starts 10 years from today)can be calculated in two steps: (1)calculate the future value of the annuity,and (2)calculate the present value of the amount determined in step (1).

Accepted Answer

The present value of a deferred annuity is calculated by first finding the future value of the annuity and then discounting that amount back to the present using the appropriate discount rate.

Question 10

If the future value of an annuity is known,then the present value of the annuity can be found using the present value of a lump sum formula,even if the amount of each annuity payment is unknown.

Accepted Answer

This is true because the present value of a lump sum formula can be used to calculate the present value of a series of cash flows, such as an annuity, even if the individual payment amounts are unknown as long as the future value and interest rate are known.

Question 11

A compound annuity involves depositing or investing a single sum of money and allowing it to compound for a certain number of years.

Accepted Answer

A compound annuity involves making regular deposits or investments over a period of time, not a single sum, and the money earns interest or grows through compounding.

Question 12

The value of a bond investment,which provides fixed interest payments,will increase when discounted at an 8% rate rather than at an 11% rate.

Accepted Answer

When the discount rate decreases, the present value of future cash flows (interest payments and principal) increases, leading to an increase in the value of the bond. Therefore, the bond investment will increase in value when discounted at a lower rate of 8% compared to 11%.

Question 13

The present value of an annuity increases as the discount rate increases.

Accepted Answer

The present value of an annuity decreases as the discount rate increases, because the higher the discount rate, the more heavily future cash flows are discounted back to the present value, resulting in a lower present value.

Question 14

You have the choice of two equally risk annuities,each paying $5,000 per year for 8 years.One is an annuity due and the other is an ordinary annuity.If you are going to be receiving the annuity payments,which annuity would you choose to maximize your wealth?

Accepted Answer

An annuity due pays at the beginning of each period, while an ordinary annuity pays at the end of each period. Because of the time value of money, receiving payments at the beginning of each period is more advantageous as the money can be invested and start earning interest immediately. Therefore, the annuity due will provide more value over the 8-year period compared to the ordinary annuity.

Question 15

The future value of an annuity due is greater than the future value of an otherwise identical ordinary annuity.

Accepted Answer

This is because in an annuity due, each payment is made at the beginning of each period, leading to one extra compounding period and therefore a higher future value compared to an ordinary annuity where payments are made at the end of each period.

Question 16

If the interest rate is positive,then the future value of an annuity due will be greater than the future value of an ordinary annuity.

Accepted Answer

This is because in an annuity due, the payments are made at the beginning of each period, which means they earn interest for one additional period compared to an ordinary annuity where payments are made at the end of each period. So, with a positive interest rate, the extra period of interest will result in a higher future value for the annuity due.

Question 17

The future value of an annuity will increase if the interest rate goes up,but the present value of the same annuity will decrease as the interest rate goes up.

Accepted Answer

The future value of an annuity increases with a higher interest rate because the payments are compounded at a higher rate, leading to a larger sum over time. Conversely, the present value decreases because each payment is discounted at a higher rate, reducing its present worth.

Question 18

Bill saves $3,000 per year in his IRA starting at age 25 and continuing to age 65,when he retires.The amount Bill has in his IRA at age 65 can be characterized as the future value of an annuity.

Accepted Answer

This is because Bill is making regular contributions to his IRA for 40 years, which creates an annuity. The future value of that annuity can be calculated using the time value of money formula.

Question 19

Two sisters each open IRAs in 2011 and plan to invest $3,000 per year for the next 30 years.Mary makes her first deposit on January 1,2011,and will make all future deposits on the first day of the year.Jane makes her first deposit on December 31,2011,and will continue to make her annual deposits on the last day of each year.At the end of 30 years,the difference in the value of the IRAs (rounded to the nearest dollar),assuming an interest rate of 7% per year,will be

Accepted Answer

Mary's IRA will earn interest for one additional year on each deposit compared to Jane's IRA, due to her making deposits at the beginning of each year. Over 30 years, with a 7% annual interest rate, this difference in compounding timing results in a significant difference in the final value of their IRAs.

Question 20

Joe borrowed $10,000 at 10% per year and promised to pay it back in equal annual installments at the end of each of the next 5 years.Joe's payment will be $2,100 [($10,000/5)+ ($10,000 × 10%)].

Accepted Answer

The calculation does not account for the decreasing principal balance over time, which affects the interest portion of the payments. The correct calculation should use the formula for an amortizing loan, which would result in different, typically decreasing, interest amounts each year and not a flat $2,100 payment.

Quiz 5: The Time Value of Money