Question 1

The future amount of an annuity due is determined ________.

Accepted Answer

The answer of The future amount of an annuity due...

Question 2

The future value of an ordinary annuity for any given interest rate and number of periods is always less than the future value of an annuity due for the same interest rate and number of periods.

Accepted Answer

The answer of The future value of an ordinary annuity...

Question 3

A specific present value of an ordinary annuity factor for a given number of periods and a specific discount rate is equal to the cumulative sum of the present value of a single sum factors over the number of periods for that discount rate.

Accepted Answer

This is true. The formula for the present value of an ordinary annuity is the sum of the present values of each individual payment, which is equal to the payment amount multiplied by the present value of a single sum factor for that particular discount rate and period. Therefore, the present value of an ordinary annuity factor is the sum of the present values of each individual payment, which is the same as the cumulative sum of the present value of a single sum factors over the number of periods for that discount rate.

Question 4

All of the following are conditions for an ordinary annuity except ________.

Accepted Answer

An ordinary annuity is a series of equal cash flows that occur at the end of each time period for a specified number of time periods. The future value of an annuity is the total value of all of the cash flows at a future point in time, while the present value of an annuity is the value of all the cash flows today. The time periods between the cash flows must be the same length, and the periodic cash flows must be equal in amount. Interest is typically compounded at the end of each time period to calculate the future value or present value of an annuity. However, the future value does not have to be equal to the present value for an ordinary annuity.

Question 5

Anne wants to accumulate $25,000 by December 31,2019.To accumulate that sum,she will make twelve equal quarterly deposits of $1,761.55 at the end of March,June,September,and December for the next three years,beginning on March 31,2016,into a fund that earns interest compounded quarterly.What annual rate of interest must the fund provide to yield the desired sum?

Accepted Answer

Using the formula for the future value of an annuity, we can calculate the total amount that Anne will have at the end of three years:

FV = PMT * ((1 + r/n)^(nt) - 1) / (r/n)

Where:
PMT = $1,761.55
n = 4 (quarterly compounding)
t = 3 (three years)
FV = $25,000

Solving for r, we get:

r = n * ((FV / PMT + 1)^(1/(n*t)) - 1)

r = 4 * ((25,000 / 1,761.55 + 1)^(1/(4*3)) - 1) = 12%

Therefore, the fund must provide an annual rate of interest of 12% to yield the desired sum of $25,000.

Question 6

Each quarter for the next 10 years,Carmen Lector will deposit $1,000 into an investment fund that pays 8% compounded quarterly.
a.How much will Carmen have at the end of 10 years if the first of 40 quarterly deposits are made at the end of each quarter?
b.How much will Carmen have at the end of 10 years if the first of 40 quarterly deposits are made at the beginning of each quarter?

Accepted Answer

The answer of Each quarter for the next 10 years,Carmen...

Question 7

A single amount is invested and increases over time as interest is compounded.If the number of periods is known,the interest rate can be approximately determined by ________.

Accepted Answer

To determine the interest rate, we need to divide the future value by the present value and look for the quotient in the future value of $1 table. This will give us the interest rate that corresponds to the number of periods.

Question 8

You are provided with two time-value-of-money tables.One table provides factors for the future value of an ordinary annuity and the other provides factors for future value of an annuity due.How can you tell which table is which type?

Accepted Answer

The answer of You are provided with two time-value-of-money tables.One...

Question 9

At the beginning of 2017,Denero Company issued 10-year bonds with a face value of $4,000,000 due on December 31,2027.The company will accumulate a fund to retire these bonds at maturity.It will make ten annual deposits to the fund beginning on December 31,2017.How much must Denero deposit each year to achieve this investment goal,assuming that it will earn 12% interest compounded annually?

Accepted Answer

To determine the required annual deposit, we need to calculate the present value of the bond's future value. Using the formula for present value of a lump sum, we get:

PV = FV / (1 + i)n
PV = $4,000,000 / (1 + 0.12)10
PV = $1,064,758.63

This means that in order to accumulate $4,000,000 by the bond's maturity date, Denero needs to deposit $1,064,758.63 in a fund earning 12% annually. To calculate the required annual deposit, we can use the formula for present value of an annuity:

PV = PMT * [1 - (1 + i)-n] / i

Solving for PMT, we get:

PMT = PV * i / [1 - (1 + i)-n]
PMT = $1,064,758.63 * 0.12 / [1 - (1 + 0.12)-10]
PMT = $227,936.72

Therefore, Denero must deposit $227,936.72 each year to accumulate enough funds to retire the bonds at maturity. The closest option to this value is choice C: $227,937.

Question 10

What is the primary difference between an ordinary annuity and an annuity due?

Accepted Answer

The primary difference between an ordinary annuity and an annuity due is the timing of the periodic payment. In an ordinary annuity, the periodic payment is made at the end of each period, while in an annuity due, the periodic payment is made at the beginning of each period. This difference in timing can have significant effects on the future value and present value of the annuity.

Question 11

Each year for the next 10 years,Carmen Lector will deposit $4,000 into an investment fund that pays 10% compounded annually.
a.How much will Carmen have at the end of 10 years if the first of 10 deposits are made at the end of each year?
b.How much will Carmen have at the end of 10 years if the first of 10 deposits are made at the beginning of each year?

Accepted Answer

The answer of Each year for the next 10 years,Carmen...

Question 12

All of the following are conditions for an annuity due except ________.

Accepted Answer

The conditions for an annuity due include equal periodic cash flows, constant interest rate, and equal time periods between cash flows. The only condition that is not true for an annuity due is that interest is compounded at the end of each time period. In an annuity due, interest is compounded at the beginning of each time period.

Question 13

Bobby's parents loaned him $80,000 to fund his college education.His parents are not charging interest.They desire to be paid one lump sum of $80,000 when Bobby can accumulate that amount.Bobby established a savings plan that earns 8% compounded annually.His new job promises to pay an annual holiday bonus that will enable him to make equal annual,year-end deposits of $6,400 starting next year.Approximately how many years will it take Bobby to accumulate the $80,000?

Accepted Answer

We can use the formula for future value of an annuity to solve this problem:
FV = Pmt x (((1 + r)^n - 1) / r)
Where FV is the future value we want to achieve ($80,000), Pmt is the annual deposit ($6,400), r is the annual interest rate (8%), and n is the number of years.
Plugging in the numbers, we get:
$80,000 = $6,400 x (((1 + 0.08)^n - 1) / 0.08)
Simplifying and solving for n, we get:
n ≈ 8.96
Therefore, it will take Bobby approximately 9 years to accumulate $80,000.

Question 14

The future value of an annuity due for any given interest rate and number of periods is always less than the future value of an annuity due for the same interest rate and number of periods.

Accepted Answer

The future value of an annuity due for any given interest rate and number of periods is always higher than the future value of an ordinary annuity for the same interest rate and number of periods. This is because in an annuity due, each payment is made at the beginning of the period, which means it has more time to earn interest compared to an ordinary annuity where each payment is made at the end of the period.

Question 15

Zendor Company wants to have $200,000 available in August 2021 to make an equipment purchase.To be able to have this amount available,Zendor will make equal annual deposits in an investment account earning 12% annually in June 2017,2018,2019,2020,and 2021.What is the dollar amount that must be deposited each of those years to achieve this objective?

Accepted Answer

We can use the formula for the future value of an annuity to solve this problem. FV = PMT x [(1 + i)^n -1]/i, where FV is the future value, PMT is the annual deposit, i is the interest rate per period, and n is the number of periods. Plugging in the given values, we get: 
$200,000 = PMT x [(1 + 0.12)^5 - 1]/0.12 
Solving for PMT, we get: 
PMT = $31,480 
Therefore, the dollar amount that must be deposited each year to achieve the objective is $31,480. The correct answer is B.

Question 16

A specific present value of an ordinary annuity factor for a given number of periods and a specific discount rate is equal to the cumulative sum of the present value of a single sum factors over all the discount rates for that specific number of periods.

Accepted Answer

The answer of A specific present value of an ordinary...

Question 17

A series of equal periodic payments in which the first payment is made one compounding period after the date of the contract is ________.

Accepted Answer

The answer of A series of equal periodic payments in...

Question 18

List the five primary characteristics of an annuity and explain the difference between an ordinary annuity and an annuity due.

Accepted Answer

The answer of List the five primary characteristics of an...

Question 19

For any discount rate and number of periods,the present value of an annuity due factor is always greater than the corresponding the present value of an ordinary annuity factor.

Accepted Answer

This is because in an annuity due, payments are made at the beginning of each period, while in an ordinary annuity, payments are made at the end of each period. As a result, the annuity due payments have an extra period to accrue interest, leading to a higher present value.

Question 20

For any discount rate,the future value of an ordinary annuity factor for n periods is equal to the future value of an annuity due factor for n - 1 periods plus 1.

Accepted Answer

This statement is true. The formula for the future value of an ordinary annuity is FV = PMT x [(1 + r)^n - 1]/r, where PMT is the periodic payment, r is the discount rate, and n is the number of periods. The future value of an annuity due is one period more than the ordinary annuity, so the formula becomes FV = PMT x [(1 + r)^n - 1]/r x (1 + r). Therefore, the future value of an ordinary annuity factor for n periods is equal to the future value of an annuity due factor for n - 1 periods plus 1.

Quiz 7: Accounting and the Time Value of Money