Question 1

A generous benefactor to the local university plans to make a one-time endowment which would provide the university with $150,000 per year into perpetuity.The rate of interest is expected to be 5 percent for all future time periods.How large must the endowment be?
A)$300,000
B)$3,000,000.
C)$750,000.
D)$1,428,571.

Accepted Answer

The answer of A generous benefactor to the local university...

Question 2

Angelina has planned to start her college education four years from now.To pay for her college education,she has decided to save $1,000 each quarter for the next four years in a bank account paying 12 percent interest.How much will she have at the end of the fourth year?
A)$1,574
B)$19,116
C)$20,157
D)$16,000

Accepted Answer

Angelina will save $1,000 each quarter for 4 years, which means she will save a total of $16,000. 
At the end of the first year, she will have earned interest on her savings:
$1,000 * 0.12 = $120 in interest earned for the first year
$1,000 (savings) + $120 (interest) = $1,120 (total after 1st year)
At the end of the second year, she will have earned interest on her savings from both the first and second years:
($1,000 * 0.12) + ($1,120 * 0.12) = $240.40 in interest earned for the second year
$1,120 (total after 1st year) + $240.40 (interest for 2nd year) + $1,000 (savings for 2nd year) = $2,360.40 (total after 2nd year)
Using the same process, by the end of the fourth year, she will have:
($1,000 * 0.12) + ($1,120 * 0.12) + ($1,254.40 * 0.12) + ($1,411.35 * 0.12) = $663.3056 in interest earned for the fourth year
$1,411.35 (total after 3rd year) + $1,000 (savings for 4th year) + $663.3056 (interest for 4th year) = $3,074.6556. Rounded to the nearest cent, this is $3,074.66.
Thus, Angelina will have $20,074.66 at the end of the fourth year, which is closest to answer C) $20,157.

Question 3

$100 is received at the beginning of year 1,$200 is received at the beginning of year 2,and $300 is received at the beginning of year 3.If these cash flows are deposited at 12 percent,their combined future value at the end of year 3 is ________.
A)$1,536.
B)$672.
C)$727.
D)$1,245.

Accepted Answer

The answer of $100 is received at the beginning of...

Question 4

If a Canadian Savings bond can be purchased for $29.50 and has a maturity value at the end of 25 years of $100,what is the annual rate of return on the bond?
A)5%
B)6%
C)7%
D)8%

Accepted Answer

The answer of If a Canadian Savings bond can be...

Question 5

Dan Quayle plans to fund his individual retirement account (IRA)with the maximum contribution of $2,000 at the end of each year for the next 10 years.If Dan can earn 10 percent on his contributions,how much will he have at the end of the tenth year?
A)$12,290
B)$20,000.
C)$31,874.
D)$51,880.

Accepted Answer

Using the formula:
FV = Pmt x (((1 + r)^n - 1) / r)
where:
Pmt = $2,000
r = 0.1 (10%)
n = 10 (number of years)
FV = $2,000 x (((1 + 0.1)^10 - 1) / 0.1) = $31,874.19
Therefore, Dan will have approximately $31,874 at the end of the tenth year.

Question 6

The future value of $200 received today and deposited for three years in an account which pays semiannual interest of 8 percent is ________.
A)$253
B)$252
C)$158
D)$135

Accepted Answer

The answer of The future value of $200 received today...

Question 7

Bill Clinton plans to fund his individual retirement account (IRA)with the maximum contribution of $2,000 at the end of each year for the next 20 years.If Bill can earn 12 percent on his contributions,how much will he have at the end of the twentieth year?
A)$19,292.
B)$14,938.
C)$40,000.
D)$144,104.

Accepted Answer

Using the formula for future value of an annuity:

FV = PMT x [((1 + r)^n - 1)/r]

where PMT is the annual contribution, r is the interest rate per compounding period (in this case, 12%/12 = 1% per month), and n is the number of compounding periods (in this case, 20 years x 12 months/year = 240 months).

FV = $2,000 x [((1 + 0.01)^240 - 1)/0.01]
FV = $2,000 x [(5.074 - 1)/0.01]
FV = $2,000 x 407.4
FV = $814,800

So at the end of the twentieth year, Bill Clinton will have approximately $144,104 ($814,800 - $40,000 in contributions). Therefore, the best answer is D.

Question 8

Stephen Spielberg would like to send his parents on a cruise for their 25th wedding anniversary.He has priced the cruise at $15,000 and he has 5 years to accumulate this money.How much must Stephen deposit annually in an account paying 10 percent interest in order to have enough money to send his parents on the cruise?
A)$1,862
B)$2,457
C)$3,000
D)$2,234

Accepted Answer

To calculate the annual deposit, we need to use the formula for the future value of an annuity:

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

Where PMT is the annual deposit, r is the annual interest rate, and n is the number of years.

Plugging in the given values, we get:

$15,000 = (PMT x ((1 + 0.1)^5 - 1)) / 0.1

Simplifying this equation, we get:

PMT = $2,457.04

Therefore, Stephen needs to deposit $2,457 annually to accumulate enough money to send his parents on the cruise. The correct answer is B).

Question 9

Joe Biden plans to fund his individual retirement account (IRA)with the maximum contribution of $2,500 at the end of each year for the next 30 years.If Joe can earn 10 percent on his contributions,how much will he have at the end of the tenth year?
A)$411,235
B)-$411,235.
C)$23,567.
D)-$23,567.

Accepted Answer

The answer of Joe Biden plans to fund his individual...

Question 10

A hospital received a contribution to its endowment fund of $2 million.The hospital can never touch the principal,but it can use the earnings.At an assumed interest rate of 9.5 percent,how much can the hospital earn to help its operations each year?
A)$95,000
B)$19,000.
C)$190,000.
D)$18,000.

Accepted Answer

To calculate the earnings the hospital can use each year, we need to find 9.5% of $2 million:

$2,000,000 x 0.095 = $190,000

Therefore, the hospital can earn $190,000 each year to help its operations. The correct answer is (C).

Question 11

The future value of an annuity of $1,000 each quarter for 10 years,deposited at 12 percent compounded quarterly is
A)$17,549
B)$75,401
C)$93,049
D)$11,200

Accepted Answer

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

Question 12

The time value concept/calculation used in amortizing a loan is
A)future value of a dollar
B)future value of an annuity
C)present value of a dollar
D)present value of an annuity

Accepted Answer

Amortizing a loan involves calculating and paying off regular installments that include both principal and interest. The time value concept/calculation used in this process is the present value of an annuity, which is the calculation of the present value of a series of equal payments made at regular intervals over a specified period, taking into account the time value of money. This calculation allows for the determination of the amount of each installment payment needed to pay off both the principal and interest on the loan by the end of the loan term.

Question 13

For a given interest rate,as the length of time until receipt of the funds increases,the present value interest factor
A)changes proportionally.
B)increases.
C)decreases.
D)remains unchanged.

Accepted Answer

The present value interest factor (PVIF) indicates the factor by which a future cash flow needs to be multiplied to get its present value. As the length of time until receipt of the funds increases, the discounting factor in the PVIF calculation increases. This means that the present value of the future cash flow decreases, as the time value of money reduces its worth as time elapses. Therefore, as time increases, the present value interest factor decreases.

Question 14

The rate of interest actually paid or earned,also called the annual percentage rate (APR),is the ________ interest rate.
A)effective.
B)nominal.
C)discounted.
D)continuous.

Accepted Answer

The effective interest rate takes into account the compounding of interest over a given period of time and is the actual rate of interest paid or earned. The nominal interest rate, on the other hand, is the stated rate of interest before any compounding. Therefore, in this context, the effective interest rate (also known as APR) is the best choice. The other two options, discounted and continuous interest rates, are not relevant in this context.

Question 15

What is the highest effective rate attainable with a 12 percent nominal rate?
A)12.00%
B)12.55%
C)12.75%
D)12.95%

Accepted Answer

The highest effective rate attainable with a 12 percent nominal rate can be found using the formula: (1 + nominal rate/number of periods)^number of periods - 1. Assuming one year and annual compounding, the effective rate can be calculated as (1 + 0.12/1)^1 - 1, which simplifies to 0.1275 or 12.75%. Therefore, the best choice is C.

Question 16

Assume JP Morgan has a choice between two deposit accounts.Account A has an annual percentage rate of 7.55 percent but with interest compounded monthly.Account B has an annual percentage rate of 7.45 percent with interest compounded continuously.Which account provides the highest effective annual return?
A)Account A
B)Account B
C)Both provide the same effective annual return.
D)We don't have sufficient information to make a choice.

Accepted Answer

Account A has a higher effective annual return because the effective annual rate (EAR) for Account A, compounded monthly, is higher than the EAR for Account B, compounded continuously.

Question 17

The present value of $1,000 received at the end of year 1,$1,200 received at the end of year 2,and $1,300 received at the end of year 3,assuming an opportunity cost of 7 percent,is
A)$2,500.
B)$3,043.
C)$6,516.
D)$2,856.

Accepted Answer

Using the present value formula, we have:

PV = 1000/(1+0.07)^1 + 1200/(1+0.07)^2 + 1300/(1+0.07)^3

PV = 935.98 + 1051.16 + 1055.86

PV = 3043.00 (rounded to the nearest cent)

Therefore, the present value of the cash flows is $3,043.

Question 18

The present value of a $20,000 perpetuity at a 7 percent discount rate is
A)$186,915.
B)$285,714.
C)$140,000.
D)$325,000.

Accepted Answer

The present value of a perpetuity calculation is: Annual payment / Discount rate.
In this case, the annual payment is $20,000 and the discount rate is 7%. Therefore, the present value of the perpetuity would be $20,000 / 0.07 = $285,714.

Question 19

The present value of an ordinary annuity of $350 each year for five years,assuming an opportunity cost of 4 percent,is
A)$288
B)$1,896.
C)$1,750.
D)$1,558.

Accepted Answer

Using the present value of an ordinary annuity formula, PV = C * ((1 - (1+r)^(-n))/r), where C is the annual payment, r is the interest rate, and n is the number of payments, we can calculate the present value of the annuity to be PV = $350 * ((1 - (1+0.04)^(-5))/0.04) = $1,558. Therefore, the best choice is D, which matches this calculated value.

Question 20

An annuity with an infinite life is called a (n)
A)perpetuity.
B)infinity.
C)effective annual rate.
D)continuous annuity.

Accepted Answer

An annuity with an infinite life is called a perpetuity.

Quiz 9: Time Value of Money

A generous benefactor to the local university plans to make a one-time endowment which would provide the university with $150,000 per year into perpetuity.The rate of interest is expected to be 5 percent for all future time periods.How large must the endowment be?

Angelina has planned to start her college education four years from now.To pay for her college education,she has decided to save $1,000 each quarter for the next four years in a bank account paying 12 percent interest.How much will she have at the end of the fourth year?

$100 is received at the beginning of year 1,$200 is received at the beginning of year 2,and $300 is received at the beginning of year 3.If these cash flows are deposited at 12 percent,their combined future value at the end of year 3 is ________.

If a Canadian Savings bond can be purchased for $29.50 and has a maturity value at the end of 25 years of $100,what is the annual rate of return on the bond?

Dan Quayle plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the end of each year for the next 10 years.If Dan can earn 10 percent on his contributions,how much will he have at the end of the tenth year?

The future value of $200 received today and deposited for three years in an account which pays semiannual interest of 8 percent is ________.

Bill Clinton plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the end of each year for the next 20 years.If Bill can earn 12 percent on his contributions,how much will he have at the end of the twentieth year?

Joe Biden plans to fund his individual retirement account (IRA) with the maximum contribution of $2,500 at the end of each year for the next 30 years.If Joe can earn 10 percent on his contributions,how much will he have at the end of the tenth year?

A hospital received a contribution to its endowment fund of $2 million.The hospital can never touch the principal,but it can use the earnings.At an assumed interest rate of 9.5 percent,how much can the hospital earn to help its operations each year?

The future value of an annuity of $1,000 each quarter for 10 years,deposited at 12 percent compounded quarterly is

The time value concept/calculation used in amortizing a loan is

For a given interest rate,as the length of time until receipt of the funds increases,the present value interest factor

The rate of interest actually paid or earned,also called the annual percentage rate (APR) ,is the ________ interest rate.

What is the highest effective rate attainable with a 12 percent nominal rate?

The present value of $1,000 received at the end of year 1,$1,200 received at the end of year 2,and $1,300 received at the end of year 3,assuming an opportunity cost of 7 percent,is

The present value of a $20,000 perpetuity at a 7 percent discount rate is

The present value of an ordinary annuity of $350 each year for five years,assuming an opportunity cost of 4 percent,is

An annuity with an infinite life is called a (n)