Question 1

To fund Jamie's lottery winnings of $17,200 per month for the next 18 years, the lottery commission needs to make a single deposit now.Assuming 9.7% compounded monthly, what should the deposit be?
Round to the nearest cent.
A)$1,753,996.94
B)$1,666,277.05
C)$1,753,995.04
D)$1,753,975.84
E)$1,753,956.94

Accepted Answer

The answer of To fund Jamie's lottery winnings of $17,200...

Question 2

One lender offers two mortgages, a 19-year mortgage at 15%, and a 23-year mortgage at 6%.For each, find the total of the monthly payments to repay $114,200.Round to the nearest cent. 
A) 19-year: $\$ 345,810.00,23$-year: $\$ 210,692.00$
B) 19-year: $\$ 345,830.88,23$-year: $\$ 210,815.29$
C) 19-year: $\$ 345,870.88,23$-year: $\$ 211,143.92$
D) 19-year: $\$ 328,539.33,23$-year: $\$ 210,815.29$
E) 19-year: $\$ 345,842.88,23$-year: $\$ 210,938.98$

Accepted Answer

For the 19-year mortgage, the monthly payment can be calculated using the formula: 
Payment = (P * r) / (1 - (1+r)^(-n*12))
where P is the principal (amount to be borrowed), r is the monthly interest rate (15%/12), and n is the number of years (19). 
Plugging in the values, we get Payment = ($114,200 * 0.15/12) / (1 - (1+0.15/12)^(-19*12)) = $2,727.88
Multiplying this by the total number of months (19*12), we get the total amount to be repaid: $345,830.88

For the 23-year mortgage, the same formula can be used with r = 6%/12 and n = 23: 
Payment = ($114,200 * 0.06/12) / (1 - (1+0.06/12)^(-23*12)) = $1,468.76
Total to be repaid: $210,815.29

Therefore, the best choice is B.

Question 3

A man estimates that the computer he plans to buy in 17 months will cost $3,600.To meet this goal, how much should he deposit in an account paying 12.7%, compounded monthly?
A)$3,014.07
B)$2,990.07
C)$2,980.07
D)$3,010.07
E)none of the above

Accepted Answer

The answer of A man estimates that the computer he...

Question 4

Assume that $800 is deposited in an account in which interest is compounded annually at a rate of 9%. Find the accumulated amount after 11 years.Round your answer to the nearest cent.
A)$2,064.34
B)$1,964.34
C)$2,164.74
D)$2,564.37
E)$2,314.36

Accepted Answer

The formula for compound interest is $A = P(1 + r)^n$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), and $n$ is the number of years the money is deposited or borrowed for. Here, $P = $800$, $r = 9\% = 0.09$, and $n = 11$ years. Plugging these values into the formula gives $A = 800(1 + 0.09)^{11} = 800(1.09)^{11} ≈ $2,064.34$.

Question 5

For a 7-day Hawaii vacation, Beth borrowed $2,450 for 6 months at an annual rate of 10.6%, compounded monthly.What did she owe?
A)$2,629.66
B)$2,582.75
C)$5,259.32
D)$3,039.65
E)$3,438.94

Accepted Answer

The answer of For a 7-day Hawaii vacation, Beth borrowed...

Question 6

The last payment of a home mortgage is a balloon payment of $21,000 which the owner is scheduled to pay in 20 years.How much extra should he start including in each monthly payment to eliminate the
Balloon payment? His mortgage is at 10.6%, compounded monthly.Round to the nearest cent.
A)$25.57
B)$51.52
C)$62.37
D)$23.01
E)$49.82

Accepted Answer

The correct answer is A because the extra payment needed to eliminate the balloon payment is $25.57. This can be calculated using the formula for the present value of an annuity, which is:PV = PMT * [1 - (1 + r)^-n] / rwhere:PV is the present value of the annuityPMT is the monthly paymentr is the monthly interest raten is the number of monthsIn this case, the present value of the annuity is $21,000, the monthly interest rate is 10.6% / 12 = 0.008833, and the number of months is 20 * 12 = 240. Plugging these values into the formula, we get:$21,000 = PMT * [1 - (1 + 0.008833)^-240] / 0.008833$21,000 = PMT * 159.684PMT = $21,000 / 159.684PMT = $25.57Therefore, the extra payment needed to eliminate the balloon payment is $25.57.

Question 7

Assume that $500 is deposited at the end of each year into an account in which interest is compounded annually at a rate of 4.5%.Find the accumulated amount after 11 years.Round to the nearest cent.
A)$6,950.04
B)$6,941.74
C)$6,878.79
D)$6,935.32
E)$6,920.59

Accepted Answer

The answer of Assume that $500 is deposited at the...

Question 8

The Jepsens are buying a $23,400 car and financing it over the next 4 years.They secure an 8.6% loan. What will their monthly payments be?
A)$564.51
B)$607.53
C)$582.35
D)$577.88

Accepted Answer

To calculate the monthly payment, we use the formula for an amortizing loan: M = P[r(1+r)^n]/[(1+r)^n – 1], where P is the principal ($23,400), r is the monthly interest rate (8.6% annual rate divided by 12 months = 0.0071667), and n is the number of payments (4 years * 12 months = 48). Plugging in these values, the monthly payment is approximately $577.88.

Question 9

Assume that $500 is deposited at the end of each year in an account in which interest is compounded annually at a rate of 8%.Find the accumulated amount after 12 years.Round to the nearest cent.
A)$9,488.56
B)$8,065.28
C)$9,988.56
D)$6,291.99
E)$6,641.99

Accepted Answer

The accumulated amount can be calculated using the future value of an annuity formula: $ FV = P \times \frac{(1 + r)^n - 1}{r} $, where $ P = 500 $, $ r = 0.08 $, and $ n = 12 $. Plugging in the values, $ FV = 500 \times \frac{(1 + 0.08)^{12} - 1}{0.08} \approx 9,488.56 $.

Question 10

The managers of a pension fund invested $2 million in government bonds paying 7.72% annual interest, compounded semiannually.After 3 years, what will the investment be worth? Round your answer to
The nearest thousand dollars.
A)$3.510 million
B)$2.510 million
C)$3.660 million
D)$5.650 million
E)none of the above

Accepted Answer

The future value of the investment can be calculated using the formula for compound interest: FV = P(1 + r/n)^(nt), where P is the principal amount ($2 million), r is the annual interest rate (0.0772), n is the number of times interest is compounded per year (2), and t is the number of years (3). Plugging in the values: FV = 2,000,000(1 + 0.0772/2)^(2*3) = 2,510,000, which rounds to $2.510 million.

Question 11

As Jorge starts working now at the age of 22, he decides to make regular contributions to a savings account.He wants to accumulate enough by age 55 to fund an annuity of $4,800 per month until age 80.
What should his monthly contributions be? Assume that both accounts pay 8.5%, compounded
Monthly.Round to the nearest cent.
A)$274.82
B)$265.82
C)$261.08
D)$270.82
E)$288.82

Accepted Answer

To calculate the monthly contributions needed, we can use the formula for the present value of an annuity:

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

Where PV is the present value of the annuity, PMT is the monthly payment, r is the monthly interest rate (8.5% / 12), and n is the total number of months (20 years x 12 months per year = 240).

We need to solve for PMT, so we can rearrange the equation:

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

The present value of the annuity is simply the future value of the annuity payments (from age 55 to 80) discounted back to the present at the same interest rate. We can use the formula for the future value of an annuity to calculate this:

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

Where FV is the future value of the annuity, PMT is the monthly payment, r is the monthly interest rate (8.5% / 12), and n is the total number of months (25 years x 12 months per year = 300).

We can plug in the given values and solve for FV:

FV = $4,800 * [(1 - (1 / (1 + 0.085/12)^300)) / (0.085/12)] * (1 + 0.085/12)^300
FV = $2,008,892.16

Now we can use this value to solve for the monthly contributions needed:

PMT = $2,008,892.16 / [(1 - (1 / (1 + 0.085/12)^240)) / (0.085/12)]
PMT = $274.82

Therefore, Jorge should make monthly contributions of $274.82 to accumulate enough savings to fund the annuity.

Question 12

Assume that $250 is deposited at the end of each period in an account in which interest is compounded at the frequency k = 3, at an annual rate of 6%.Find the accumulated amount after 8 years.Round to the
Nearest cent.
A)$7,626.77
B)$7,580.90
C)$7,605.47
D)$7,556.32
E)$7,591.32

Accepted Answer

The annual interest rate is 6%, so the quarterly interest rate is $(1 + 0.06)^{1/3} \approx 1.01877$. Using the formula for the future value of an annuity:

$FV = P\frac{(1 + r)^{nk} - 1}{r}$
where $P$ is the periodic payment, $r$ is the interest rate per period, $n$ is the number of years, and $k$ is the number of compounding periods per year.

Substituting the given values, we have:

$FV = 250\frac{(1 + 0.01877)^{8\cdot3} - 1}{0.01877}$

$FV \approx 7,605.47$

Rounding to the nearest cent, we get the final answer of $\boxed{	extbf{(C) }7,605.47}$.

Question 13

What single amount deposited now into an account paying $7 \frac { 2 } { 3 } \%$ annual interest, compounded quarterly, would fund an annuity paying $\$ 3,470$ quarterly for the next 18 years?
A) $\$ 134,873.15$
B) $\quad \$ 135,031.34$
C) $\$ 134,917.86$
D) $\quad \$ 134,898.15$

Accepted Answer

The answer of What single amount deposited now into an...

Question 14

Bank One offers a passbook account with a 4.35% annual rate, compounded quarterly.Bank Two offers a money market account at 4%, compounded monthly.Find the better growth by calculating the
Effective rates.What is the greater effective rate?
A)0.04%
B)0.04%.
C)4.07%
D)4.42%
E)none of the above

Accepted Answer

To calculate the effective rate, we use the formula (1 + (r/n))^n - 1, where r is the annual rate and n is the number of times compounded per year.

For Bank One:
Effective rate = (1 + (0.0435/4))^4 - 1 = 0.0442 or 4.42%

For Bank Two:
Effective rate = (1 + (0.04/12))^12 - 1 = 0.0407 or 4.07%

Therefore, Bank One has the greater effective rate and is the better choice.

Note: Option A and B are duplicates.

Question 15

When Jim retires in 14 years, he expects to live lavishly on the money in a retirement account that is earning 9% interest, compounded semiannually.If the account now contains $147,000, how much will
Be available at retirement?
A)$505,166.02
B)$504,265.90
C)$504,266.24
D)$504,165.90
E)$579,790.79

Accepted Answer

The answer of When Jim retires in 14 years, he...

Question 16

Assume that $1,500 is deposited in an account in which interest is compounded annually at a rate of 8%.Find the accumulated amount after 14 years rounded to the nearest cent.
A)$4,805.79
B)$4,505.79
C)$4,355.79
D)$4,305.79
E)$4,405.79

Accepted Answer

The answer of Assume that $1,500 is deposited in an...

Question 17

At the birth of their child, the Fieldsons deposited $5000 in an account paying 8% interest, compounded quarterly.How much will be available when the child turns 11?
A)$11,849.73
B)$12,250.67
C)$5,975.14
D)$12,050.81
E)$11,950.27

Accepted Answer

The answer of At the birth of their child, the...

Question 18

Assume that $1,500 is deposited in an account in which interest is compounded 8 times a year, at an annual rate of 5%.Find the accumulated amount after 12 years.Round your answer to the nearest cent.
A)$2,628.08
B)$2,828.08
C)$2,678.08
D)$3,028.08
E)$2,728.08

Accepted Answer

The answer of Assume that $1,500 is deposited in an...

Question 19

Property in suburbs closer to the city is appreciating about 7.5% annually.If this trend continues, what will a $36,000 one-acre lot be worth in five years? Give the result to the nearest dollar.
A)$56,004
B)$52,917
C)$51,683
D)$52,300
E)$52,895

Accepted Answer

The answer of Property in suburbs closer to the city...

Question 20

Find the present value of an annuity with annual payments of $3,250 at 5.45%, compounded annually for 24 years.Round to the nearest cent. 
A) $\quad P V = \$ 42,961.75$
B) $\quad P V = \$ 40,799.07$
C) $\quad P V = \$ 82,251.00$
D) $\quad P V = \$ 42,946.39$
E) $\quad P V = \$ 42,931.03$

Accepted Answer

To find the present value of an annuity, we can use the formula:

PV = A * ((1 - (1 + r)^(-n)) / r)

where PV is the present value, A is the annual payment, r is the annual interest rate expressed as a decimal, and n is the number of years.

Plugging in the given values, we get:

PV = 3,250 * ((1 - (1 + 0.0545)^(-24)) / 0.0545)
PV ≈ $42,946.39

Therefore, the answer is D, with a present value of $42,946.39.

Quiz 9: Natural Number Functions and Probability

To fund Jamie's lottery winnings of $17,200 per month for the next 18 years, the lottery commission needs to make a single deposit now.Assuming 9.7% compounded monthly, what should the deposit be? Round to the nearest cent.

One lender offers two mortgages, a 19-year mortgage at 15%, and a 23-year mortgage at 6%.For each, find the total of the monthly payments to repay $114,200.Round to the nearest cent.

A man estimates that the computer he plans to buy in 17 months will cost $3,600.To meet this goal, how much should he deposit in an account paying 12.7%, compounded monthly?

Assume that $800 is deposited in an account in which interest is compounded annually at a rate of 9%. Find the accumulated amount after 11 years.Round your answer to the nearest cent.

For a 7-day Hawaii vacation, Beth borrowed $2,450 for 6 months at an annual rate of 10.6%, compounded monthly.What did she owe?

The last payment of a home mortgage is a balloon payment of $21,000 which the owner is scheduled to pay in 20 years.How much extra should he start including in each monthly payment to eliminate the Balloon payment? His mortgage is at 10.6%, compounded monthly.Round to the nearest cent.

Assume that $500 is deposited at the end of each year into an account in which interest is compounded annually at a rate of 4.5%.Find the accumulated amount after 11 years.Round to the nearest cent.

The Jepsens are buying a $23,400 car and financing it over the next 4 years.They secure an 8.6% loan. What will their monthly payments be?

Assume that $500 is deposited at the end of each year in an account in which interest is compounded annually at a rate of 8%.Find the accumulated amount after 12 years.Round to the nearest cent.

The managers of a pension fund invested $2 million in government bonds paying 7.72% annual interest, compounded semiannually.After 3 years, what will the investment be worth? Round your answer to The nearest thousand dollars.

Assume that $250 is deposited at the end of each period in an account in which interest is compounded at the frequency k = 3, at an annual rate of 6%.Find the accumulated amount after 8 years.Round to the Nearest cent.

What single amount deposited now into an account paying 723%7 \frac { 2 } { 3 } \%732​% annual interest, compounded quarterly, would fund an annuity paying $3,470\$ 3,470$3,470 quarterly for the next 18 years?

Bank One offers a passbook account with a 4.35% annual rate, compounded quarterly.Bank Two offers a money market account at 4%, compounded monthly.Find the better growth by calculating the Effective rates.What is the greater effective rate?

When Jim retires in 14 years, he expects to live lavishly on the money in a retirement account that is earning 9% interest, compounded semiannually.If the account now contains $147,000, how much will Be available at retirement?

Assume that $1,500 is deposited in an account in which interest is compounded annually at a rate of 8%.Find the accumulated amount after 14 years rounded to the nearest cent.

At the birth of their child, the Fieldsons deposited $5000 in an account paying 8% interest, compounded quarterly.How much will be available when the child turns 11?

Assume that $1,500 is deposited in an account in which interest is compounded 8 times a year, at an annual rate of 5%.Find the accumulated amount after 12 years.Round your answer to the nearest cent.

Property in suburbs closer to the city is appreciating about 7.5% annually.If this trend continues, what will a $36,000 one-acre lot be worth in five years? Give the result to the nearest dollar.

Find the present value of an annuity with annual payments of $3,250 at 5.45%, compounded annually for 24 years.Round to the nearest cent.

What single amount deposited now into an account paying $7 \frac { 2 } { 3 } \%$ annual interest, compounded quarterly, would fund an annuity paying $\$ 3,470$ quarterly for the next 18 years?