Question 1

Find the periodic payment required to repay $27,480 over 12 years, with monthly payments at a 9% annual rate.Round to the nearest cent. 
A) $\quad P = \$ 400.25$
B) $\quad P = \$ 444.01$
C) $\quad P = \$ 312.73$
D) $\quad P = \$ 268.97$
E) none of the above

Accepted Answer

First, we need to find the monthly interest rate by dividing the annual rate by 12:

$0.09/12 = 0.0075$

Next, we need to find the total number of payments over 12 years:

$12 	ext{ years} 	imes 12 	ext{ months/year} = 144 	ext{ months}$

Now, we can use the formula for the monthly payment on a loan:

$P = \dfrac{r(PV)}{1-(1+r)^{-n}}$

where:
$P = 	ext{monthly payment}$
$r = 	ext{monthly interest rate}$
$PV = 	ext{present value or amount borrowed}$
$n = 	ext{number of payments}$

Plugging in the values we have:

$P = \dfrac{0.0075(27480)}{1-(1+0.0075)^{-144}} \approx \boxed{\$312.73}$

Therefore, the best choice is C, with a monthly payment of $312.73.

Question 2

Assume that $200 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 14 years.Round to the nearest cent.
A)$3,814.02
B)$3,786.42
C)$3,750.12
D)$3,800.22
E)$3,819.92

Accepted Answer

The answer of Assume that $200 is deposited at the...

Question 3

Bank One offers a passbook account with a 3.55% annual rate, compounded quarterly.Bank Two offers a money market account at 3.5%, compounded monthly.Find the better growth by calculating the
Effective rates.What is the greater effective rate?
A)3.60%
B)3.56%
C)0.04%
D)0.04%.
E)none of the above

Accepted Answer

We can calculate the effective rate for Bank One using the formula: 
Effective rate = (1 + (annual rate / n))^n - 1, where n is the number of times compounded per year. 
Plugging in the numbers, we get: 
Effective rate for Bank One = (1 + (0.0355 / 4))^4 - 1 = 0.0360 or 3.60%

Similarly, we can calculate the effective rate for Bank Two as:
Effective rate for Bank Two = (1 + (0.035 / 12))^12 - 1 = 0.0356 or 3.56%

Comparing the two, we can see that the better growth is offered by Bank One with an effective rate of 3.60%. Therefore, the best choice would be Bank One.

Question 4

The managers of a pension fund invested $5 million in government bonds paying 6.83% annual interest, compounded semiannually.After 3 years, what will the investment be worth? Round your answer to
The nearest thousand dollars.
A)$7.266 million
B)$6.116 million
C)$7.116 million
D)$9.256 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 ($5 million), r is the annual interest rate (0.0683), n is the number of times interest is compounded per year (2 for semiannual), and t is the number of years (3). Plugging in these values, FV = 5,000,000(1 + 0.0683/2)^(2*3) = $6,116,000, which rounds to $6.116 million.

Question 5

Jim will retire in 30 years.He will invest $100 each month for 15 years and then let the accumulated value continue to grow for the next 15 years.How much will be available at retirement? Assume 9%,
Compounded monthly.Round to the nearest dollar.
A)$130,692
B)$145,234
C)$139,399
D)$145,207
E)$138,014

Accepted Answer

To solve this problem we need to use the formula for future value of an annuity:

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

where FV is the future value, PMT is the monthly investment amount, r is the interest rate per month (9%/12), and n is the total number of months (15 years x 12 months/year = 180 months).

Using this formula, we can calculate the future value of Jim's investments after 15 years:

FV = 100 x (((1 + 0.0075)^180 - 1) / 0.0075) = $30,687

This means that after 15 years, Jim will have $30,687 saved up.

Next, we need to calculate the future value of this amount after another 15 years of compounding at 9% per year. To do this, we can use the formula for future value of a lump sum:

FV = PV x (1 + r)^n

where PV is the present value (in this case, $30,687), r is the interest rate per year (9%), and n is the total number of years (15).

Using this formula, we get:

FV = 30,687 x (1 + 0.09)^15 = $145,234

So the total amount available at retirement will be $145,234.

Therefore, the best choice is B.

Question 6

Property in suburbs closer to the city is appreciating about 9% annually.If this trend continues, what will a $46,000 one-acre lot be worth in five years? Give the result to the nearest dollar.
A)$75,098
B)$71,394
C)$70,777
D)$72,011
E)$71,989

Accepted Answer

Using the formula for exponential growth: 
A = P(1+r)^t 
where A is the final amount, P is the initial amount, r is the annual growth rate as a decimal, and t is the number of years. 
Plugging in the values: 
A = 46,000(1+0.09)^5 
A = 46,000(1.09)^5 
A ≈ 70,777 
Rounding to the nearest dollar gives the answer of choice C, $70,777.

Question 7

Assume that $\$ 350$ is deposited at the end of each year into an account in which interest is compounded annually at a rate of $8.5 \%$. Find the accumulated amount after 3 years. Round to the nearest cent.
A)$1,106.38
B)$1,101.03
C)$1,164.63
D)$1,141.78
E)$1,187.48
​

Accepted Answer

The future value of an annuity formula is used: $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $P = 350$, $r = 0.085$, and $n = 3$. Calculating gives $FV = 350 \times \frac{(1 + 0.085)^3 - 1}{0.085} = 1,141.78$.

Question 8

Find the amount of each regular payment to provide $6,500 in 6 years, at an annual rate r = 7%, compounded annually.
A)$914.85
B)$921.02
C)$924.52
D)$892.72
E)$908.67

Accepted Answer

The answer of Find the amount of each regular payment...

Question 9

Property values in the suburbs have been appreciating about 11% annually.If this trend continues, what will a $180,000 home be worth in four years? Give the result to the nearest dollar.
A)$549,927
B)$273,253
C)$276,674
D)$274,487
E)$274,253

Accepted Answer

The answer of Property values in the suburbs have been...

Question 10

Find the amount of each regular payment to provide $21,000 in 10 years, at an annual rate r = 6%, compounded semiannually.
A)$798.43
B)$804.23
C)$781.53
D)$792.88
E)$795.03

Accepted Answer

The answer of Find the amount of each regular payment...

Question 11

Find the present value of $70,000 due in 8 years, given an annual rate of 8% compounded quarterly. Round tour answer to the nearest cent.
A)$37,244.73
B)$36,843.68
C)$37,044.33
D)$37,144.33
E)$37,144.53

Accepted Answer

The answer of Find the present value of $70,000 due...

Question 12

Assume that $100 is deposited at the end of each year in an account in which interest is compounded annually at a rate of 10%.Find the accumulated amount after 4 years.Round to the nearest cent.
A)$464.10
B)$614.10
C)$364.10
D)$564.10
E)none of the above

Accepted Answer

The future value of an annuity is given by the formula:FV = P * ((1 + r)^n - 1) / rwhere:P is the amount of each paymentr is the annual interest raten is the number of yearsIn this case, P = 100, r = 0.10, and n = 4. Plugging these values into the formula, we get:FV = 100 * ((1 + 0.10)^4 - 1) / 0.10= 100 * (1.4641 - 1) / 0.10= 100 * 0.4641= 46.41Rounding to the nearest cent, the accumulated amount after 4 years is $464.10.

Question 13

Assume that $500 is deposited at the end of each year in an account in which interest is compounded annually at a rate of 7%.Find the accumulated amount after 6 years.Round to the nearest cent.
A)$3,589.10
B)$3,597.55
C)$3,601.55
D)$3,576.65
E)$3,559.30

Accepted Answer

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

Question 14

When Jim retires in 9 years, he expects to live lavishly on the money in a retirement account that is earning 8% interest, compounded semiannually.If the account now contains $152,500, how much will
Be available at retirement?
A)$309,037.36
B)$309,937.14
C)$308,937.02
D)$309,037.02
E)$355,277.57

Accepted Answer

The answer of When Jim retires in 9 years, he...

Question 15

Find the periodic payment required to repay $1,220 repaid in 3 monthly installments, at an annual rate of 14%.Round to the nearest cent. 
A)$\quad P = \$ 374.57$
B) $\quad P = \$ 832.38$
C) $P = \$ 37.03$
D) $\quad P = \$ 463.80$
E) $P = \$ 416.19$

Accepted Answer

The periodic payment can be calculated using the formula for an ordinary annuity. The monthly interest rate is 14%/12 = 1.1667%. Using the formula, the payment is approximately $416.19.

Question 16

Find the amount of each regular payment to provide $12,500 in 15 years, at an annual rate r = 6%, compounded quarterly.
A)$203.92
B)$143.62
C)$137.17
D)$129.92
E)$141.97

Accepted Answer

The answer of Find the amount of each regular payment...

Question 17

Assume that $300 is deposited at the end of each year in an account in which interest is compounded annually at a rate of 9%.Find the accumulated amount after 10 years.Round to the nearest cent.
A)$4,557.88
B)$4,857.88
C)$1,419.29
D)$3,038.59
E)$1,519.29

Accepted Answer

The accumulated amount can be calculated using the future value of an annuity formula: $ FV = P \frac{(1 + r)^n - 1}{r} $, where $ P = 300 $, $ r = 0.09 $, and $ n = 10 $. Plugging in these values gives $ FV = 300 \frac{(1 + 0.09)^{10} - 1}{0.09} \approx 4,557.88 $.

Question 18

Find the present value of an annuity with semiannual payments of $400 at 4.22%, compounded semiannually for 15 years.Round to the nearest cent. 
A) $\quad P V = \$ 8,824.55$
B) $\quad P V = \$ 12,253.20$
C) $\quad P V = \$ 16,509.77$
D) $\quad P V = \$ 9,707.01$
E) $\quad P V = \$ 17,649.10$

Accepted Answer

We need to use the formula $PV = \dfrac{PMT}{r} \left(1-\dfrac{1}{(1+r)^n} \right)$ where $PMT$ is the semiannual payment amount, $r$ is the semiannual interest rate (which is $4.22\%/2 = 0.0211$), and $n$ is the total number of semiannual payments (which is $2\cdot 15 = 30$). Plugging in the values, we get $PV = \dfrac{400}{0.0211} \left(1-\dfrac{1}{(1+0.0211)^{30}} \right) \approx \$ 8,824.55$, rounded to the nearest cent. Thus, the best answer is A.

Question 19

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 $6,500 per month until age 80.
What should his monthly contributions be? Assume that both accounts pay 8.75%, compounded
Monthly.Round to the nearest cent.
A)$357.94
B)$326.74
C)$343.94
D)$334.94
E)$339.94

Accepted Answer

The answer of As Jorge starts working now at the...

Question 20

The Jepsens are buying a $22,800 car and financing it over the next 6 years.They secure a 6.5% loan. What will be the total of the monthly payments? Round to the nearest cent.
A)$23,455.90
B)$27,595.18
C)$9,198.39
D)$82,785.54
E)$13,797.59

Accepted Answer

To find the monthly payment, we need to use the formula for the fixed payment on a loan:

M = P * (r(1+r)^n)/((1+r)^n - 1)

Where:
M = monthly payment
P = principal (loan amount)
r = monthly interest rate (6.5% / 12 = 0.00541667)
n = number of payments (6 years * 12 months/year = 72)

Substituting in our values:

M = 22,800 * (0.00541667(1+0.00541667)^72)/((1+0.00541667)^72-1)
M = $384.14

However, we need to round to the nearest cent and also find the total of the monthly payments over 6 years, so we need to multiply this by the number of payments:

Total = 384.14 * 72
Total = $27,595.18

Therefore, the best choice is B.

Quiz 9: Natural Number Functions and Probability

Find the periodic payment required to repay $27,480 over 12 years, with monthly payments at a 9% annual rate.Round to the nearest cent.

Assume that $200 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 14 years.Round to the nearest cent.

Bank One offers a passbook account with a 3.55% annual rate, compounded quarterly.Bank Two offers a money market account at 3.5%, compounded monthly.Find the better growth by calculating the Effective rates.What is the greater effective rate?

The managers of a pension fund invested $5 million in government bonds paying 6.83% annual interest, compounded semiannually.After 3 years, what will the investment be worth? Round your answer to The nearest thousand dollars.

Jim will retire in 30 years.He will invest $100 each month for 15 years and then let the accumulated value continue to grow for the next 15 years.How much will be available at retirement? Assume 9%, Compounded monthly.Round to the nearest dollar.

Property in suburbs closer to the city is appreciating about 9% annually.If this trend continues, what will a $46,000 one-acre lot be worth in five years? Give the result to the nearest dollar.

Assume that $\$ 350$ is deposited at the end of each year into an account in which interest is compounded annually at a rate of $8.5 \%$ . Find the accumulated amount after 3 years. Round to the nearest cent.

Find the amount of each regular payment to provide $6,500 in 6 years, at an annual rate r = 7%, compounded annually.

Property values in the suburbs have been appreciating about 11% annually.If this trend continues, what will a $180,000 home be worth in four years? Give the result to the nearest dollar.

Find the amount of each regular payment to provide $21,000 in 10 years, at an annual rate r = 6%, compounded semiannually.

Find the present value of $70,000 due in 8 years, given an annual rate of 8% compounded quarterly. Round tour answer to the nearest cent.

Assume that $100 is deposited at the end of each year in an account in which interest is compounded annually at a rate of 10%.Find the accumulated amount after 4 years.Round to the nearest cent.

Assume that $500 is deposited at the end of each year in an account in which interest is compounded annually at a rate of 7%.Find the accumulated amount after 6 years.Round to the nearest cent.

When Jim retires in 9 years, he expects to live lavishly on the money in a retirement account that is earning 8% interest, compounded semiannually.If the account now contains $152,500, how much will Be available at retirement?

Find the periodic payment required to repay $1,220 repaid in 3 monthly installments, at an annual rate of 14%.Round to the nearest cent.

Find the amount of each regular payment to provide $12,500 in 15 years, at an annual rate r = 6%, compounded quarterly.

Assume that $300 is deposited at the end of each year in an account in which interest is compounded annually at a rate of 9%.Find the accumulated amount after 10 years.Round to the nearest cent.

Find the present value of an annuity with semiannual payments of $400 at 4.22%, compounded semiannually for 15 years.Round to the nearest cent.

The Jepsens are buying a $22,800 car and financing it over the next 6 years.They secure a 6.5% loan. What will be the total of the monthly payments? Round to the nearest cent.

Quiz 9: Natural Number Functions and Probability

Find the periodic payment required to repay $27,480 over 12 years, with monthly payments at a 9% annual rate.Round to the nearest cent.

Assume that $200 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 14 years.Round to the nearest cent.

Bank One offers a passbook account with a 3.55% annual rate, compounded quarterly.Bank Two offers a money market account at 3.5%, compounded monthly.Find the better growth by calculating the Effective rates.What is the greater effective rate?

The managers of a pension fund invested $5 million in government bonds paying 6.83% annual interest, compounded semiannually.After 3 years, what will the investment be worth? Round your answer to The nearest thousand dollars.

Jim will retire in 30 years.He will invest $100 each month for 15 years and then let the accumulated value continue to grow for the next 15 years.How much will be available at retirement? Assume 9%, Compounded monthly.Round to the nearest dollar.

Property in suburbs closer to the city is appreciating about 9% annually.If this trend continues, what will a $46,000 one-acre lot be worth in five years? Give the result to the nearest dollar.

Assume that $350\$ 350$350 is deposited at the end of each year into an account in which interest is compounded annually at a rate of 8.5%8.5 \%8.5% . Find the accumulated amount after 3 years. Round to the nearest cent.

Find the amount of each regular payment to provide $6,500 in 6 years, at an annual rate r = 7%, compounded annually.

Property values in the suburbs have been appreciating about 11% annually.If this trend continues, what will a $180,000 home be worth in four years? Give the result to the nearest dollar.

Find the amount of each regular payment to provide $21,000 in 10 years, at an annual rate r = 6%, compounded semiannually.

Find the present value of $70,000 due in 8 years, given an annual rate of 8% compounded quarterly. Round tour answer to the nearest cent.

Assume that $100 is deposited at the end of each year in an account in which interest is compounded annually at a rate of 10%.Find the accumulated amount after 4 years.Round to the nearest cent.

Assume that $500 is deposited at the end of each year in an account in which interest is compounded annually at a rate of 7%.Find the accumulated amount after 6 years.Round to the nearest cent.

When Jim retires in 9 years, he expects to live lavishly on the money in a retirement account that is earning 8% interest, compounded semiannually.If the account now contains $152,500, how much will Be available at retirement?

Find the periodic payment required to repay $1,220 repaid in 3 monthly installments, at an annual rate of 14%.Round to the nearest cent.

Find the amount of each regular payment to provide $12,500 in 15 years, at an annual rate r = 6%, compounded quarterly.

Assume that $300 is deposited at the end of each year in an account in which interest is compounded annually at a rate of 9%.Find the accumulated amount after 10 years.Round to the nearest cent.

Find the present value of an annuity with semiannual payments of $400 at 4.22%, compounded semiannually for 15 years.Round to the nearest cent.

The Jepsens are buying a $22,800 car and financing it over the next 6 years.They secure a 6.5% loan. What will be the total of the monthly payments? Round to the nearest cent.

Assume that $\$ 350$ is deposited at the end of each year into an account in which interest is compounded annually at a rate of $8.5 \%$ . Find the accumulated amount after 3 years. Round to the nearest cent.