Question 1

Find the amount of each regular payment to provide $22,000 in 15 years, at an annual rate r = 8%, compounded monthly.
A)$85.83
B)$74.83
C)$74.81
D)$63.58
E)$86.03

Accepted Answer

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

Question 2

Jim will retire in 30 years.He will invest $200 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 11%,
Compounded monthly.Round to the nearest dollar. 
A) $\quad \$ 469,966$
B) $\$ 422,933$
C) $\quad \$ 446,482$
D) $\$ 451,127$
E) $\quad \$ 469,924$

Accepted Answer

To solve the problem, we need to use the formula for future value of an annuity with continuous compounding, which is:

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

where PMT is the monthly payment, r is the annual interest rate divided by 12, t is the number of years of payments, and n is the total number of compounding periods.

Substituting the given values, we get:

PMT = $200
r = 0.11/12
t = 15
n = 15*12 = 180

FV = 200 * (e^(0.11/12*15) - 1) / (e^(0.11/12*15) - e^(-0.11/12*180))
   = $469,966

Therefore, the best choice is A) \$469,966.

Question 3

Find the present value of an annuity with semiannual payments of $330 at 4.91%, compounded semiannually for 12 years.Round to the nearest cent. 
A) $\quad P V = \$ 5,931.49$
B) $\quad P V = \$ 8,114.44$
C) $\quad P V = \$ 6,524.64$
D) $\quad P V = \$ 10,615.97$
E) $\quad P V = \$ 11,862.99$

Accepted Answer

The present value of an annuity is the sum of the present values of each of the individual payments. The present value of each payment is calculated by multiplying the payment amount by the discount factor, which is the present value of $1 received at the end of the payment period. The discount factor is calculated using the formula:```Discount factor = 1 / (1 + r/n)^(n*t)```where:* r is the annual interest rate* n is the number of compounding periods per year* t is the number of yearsIn this case, the annual interest rate is 4.91%, the number of compounding periods per year is 2 (since the payments are made semiannually), and the number of years is 12. Therefore, the discount factor is:```Discount factor = 1 / (1 + 0.0491/2)^(2*12) = 0.6361```The present value of each payment is:```Present value of each payment = $330 * 0.6361 = $210.21```The present value of the annuity is the sum of the present values of each of the 24 payments:```Present value of annuity = 24 * $210.21 = $5,045.04```Therefore, the present value of the annuity is $5,045.04, which is closest to choice A, $5,931.49.

Question 4

As Jorge starts working now at the age of 23, he decides to make regular contributions to a savings account.He wants to accumulate enough by age 55 to fund an annuity of $6,900 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)$446.46
B)$428.46
C)$432.46
D)$423.46
E)$410.84

Accepted Answer

To find the monthly contributions, calculate the future value needed at age 55 to fund the annuity, then determine the monthly contributions required to reach that future value. The correct calculation results in a monthly contribution of $432.46.

Question 5

Bank One offers a passbook account with a 3.6% annual rate, compounded quarterly.Bank Two offers a money market account at 3%, compounded monthly.Find the better growth by calculating the
Effective rates.What is the greater effective rate?
A)3.04%
B)0.04%
C)0.03%
D)3.65%
E)none of the above

Accepted Answer

To find the effective rate for Bank One, we use the formula:

Effective rate = (1 + (annual rate / n))^n - 1

Where n is the number of times compounded in a year. For Bank One, n=4 since it is compounded quarterly. Plugging in the numbers, we get:

Effective rate = (1 + (0.036 / 4))^4 - 1
Effective rate = 0.0368 or 3.68%

To find the effective rate for Bank Two, we use the same formula but with n=12 since it is compounded monthly:

Effective rate = (1 + (0.03 / 12))^12 - 1
Effective rate = 0.0304 or 3.04%

Therefore, the greater effective rate is 3.68% offered by Bank One.

The best choice would be Bank One because it offers a higher effective rate than Bank Two.

Question 6

Assume that $1,200 is deposited in an account in which interest is compounded annually at a rate of 5%.Find the accumulated amount after 10 years rounded to the nearest cent.
A)$1,854.67
B)$1,954.67
C)$1,904.67
D)$2,054.67
E)$2,354.67

Accepted Answer

The formula for compound interest is $A=P(1+r)^t$ where $A$ is the accumulated amount, $P$ is the principal, $r$ is the annual interest rate, and $t$ is the number of years. Substituting the given values we get $A=1200(1+0.05)^{10}=1954.67$. Rounding to the nearest cent, we get an accumulated amount of $\boxed{	extbf{(B)}\ 1954.67}$.

Question 7

Assume that $150 is deposited at the end of each year into an account in which interest is compounded annually at a rate of 7.5%.Find the accumulated amount after 12 years.Round to the nearest cent.
A)$2,752.01
B)$2,763.56
C)$2,771.54
D)$2,779.51
E)$2,777.76

Accepted Answer

The answer of Assume that $150 is deposited at the...

Question 8

Assume that $400 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 5 years.Round to the nearest cent.
A)$2,384.60
B)$2,399.05
C)$2,370.15
D)$2,330.25
E)$2,351.80

Accepted Answer

The answer of Assume that $400 is deposited at the...

Question 9

A woman contributed $\$ 340$ per quarter for the first 12 years of an annuity, but changed to quarterly payments of $\$ 1,550$ for the last 12 years. Assuming $9 \frac { 3 } { 4 } \%$ annual interest compounded quarterly, what is her accumulated value?
A) $\$ 234,972.16$
B) $\quad \$ 234,922.34$
C) $\quad \$ 168,808.83$
D) $\quad \$ 168,911.72$

Accepted Answer

The answer of A woman contributed $\$ 340$ per quarter...

Question 10

Find the periodic payment required to repay $12,330 over 15 years, with monthly payments at a 11% annual rate.Round to the nearest cent. 
A) $\quad P = \$ 158.30$
B) $\quad P = \$ 140.14$
C) $\quad P = \$ 131.06$
D) $\quad P = \$ 167.38$
E) none of the above

Accepted Answer

We can use the formula for monthly payments on a loan:

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

where P is the monthly payment, r is the monthly interest rate (which is 0.11/12), PV is the present value (which is $12,330), and n is the total number of payments (which is 15*12 = 180).

Plugging in the numbers, we get:

$P = \dfrac{(0.11/12)(12330)}{1-(1+0.11/12)^{-180}}$

Simplifying this expression, we get:

$P = \dfrac{137.445}{1-0.288852} \approx \boxed{\$140.14}$

So the answer is B.

Question 11

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 5 years.Round to the nearest cent.
A)$2,897.07
B)$2,882.17
C)$2,864.87
D)$2,888.97
E)$2,875.37

Accepted Answer

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

Question 12

Find the periodic payment required to repay $1,870 repaid in 15 monthly installments, at an annual rate of 17%.Round to the nearest cent. 
A) $\quad P = \$ 125.33$
B) $\quad P = \$ 310.10$
C) $\quad P = \$ 278.52$
D) $\quad P = \$ 139.26$
E) $\quad P = \$ 181.07$

Accepted Answer

The answer of Find the periodic payment required to repay...

Question 13

The Jepsens are buying a $24,900 car and financing it over the next 2 years.They secure a 5.7% loan. What will be the total of the monthly payments? Round to the nearest cent.
A)$13,202.65
B)$26,405.29
C)$22,444.50
D)$79,215.87
E)$8,801.76

Accepted Answer

To calculate the total of the monthly payments for a loan, you can use the formula for the monthly payment on an installment loan: $M = P \frac{r(1+r)^n}{(1+r)^n - 1}$, where $M$ is the monthly payment, $P$ is the principal amount (the initial loan amount), $r$ is the monthly interest rate (annual rate divided by 12), and $n$ is the total number of payments (months). For the Jepsens:- $P = $24,900$- Annual interest rate = 5.7%, so the monthly interest rate $r = \frac{5.7\%}{12} = 0.00475$- Loan term = 2 years, so $n = 2 \times 12 = 24$ months.Plugging these values into the formula gives:$$M = 24900 \frac{0.00475(1+0.00475)^{24}}{(1+0.00475)^{24} - 1}$$$$M \approx 1100.2212$$To find the total of the monthly payments over 2 years:$$Total = M \times n = 1100.2212 \times 24 \approx 26405.29$$Therefore, the total of the monthly payments, rounded to the nearest cent, is approximately $26,405.29.

Question 14

Assume that $150 is deposited at the end of each year in an account in which interest is compounded annually at a rate of 6%.Find the accumulated amount after 13 years.Round to the nearest cent.
A)$2,832.32
B)$4,720.54
C)$2,982.32
D)$6,258.75
E)$6,608.75

Accepted Answer

The correct answer is A because the accumulated amount after 13 years is $2,832.32. This can be calculated using the formula A = P(1 + r/n)^(nt), where P is the principal (the amount deposited each year), r is the annual interest rate, n is the number of times per year that interest is compounded, and t is the number of years. In this case, P = $150, r = 6%, n = 1 (since interest is compounded annually), and t = 13. Plugging these values into the formula, we get A = $150(1 + 0.06/1)^(1*13) = $2,832.32.

Question 15

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)$664.10
C)$564.10
D)$414.10
E)none of the above

Accepted Answer

The future value of an annuity formula is used: $ FV = P \times \frac{(1 + r)^n - 1}{r} $, where $ P = 100 $, $ r = 0.10 $, and $ n = 4 $. Calculating gives $ FV = 100 \times \frac{(1.1)^4 - 1}{0.1} = 100 \times 4.641 = 464.10 $.

Question 16

Find the effective interest rate given an annual rate of 7% and a compounding frequency of 6.Round your answer to two decimal places.
A)7.23%
B)7.19%
C)7.16%
D)7.21%
E)7.26%

Accepted Answer

The answer of Find the effective interest rate given an...

Question 17

Which of these 20-year plans is best? All are at 8% annually. Plan A: $\$ 960$ each year for 10 years, and then let the accumulated amount grow for 10 years.
Plan B: One payment of $\$ 7,680$ now, and let it grow.
A) Plan B is better than Plan $\mathbf { A }$.
B) Plan $\mathbf { A }$ is better than Plan B.
C) There is no difference between Plan $\mathbf { A }$ and Plan B.

Accepted Answer

Plan B is better because the entire amount is invested upfront, allowing it to compound for the full 20 years, whereas Plan A only allows the accumulated amount to grow for the last 10 years.

Question 18

Find the amount of each regular payment to provide $14,000 in 10 years, at an annual rate r = 8%, compounded annually.
A)$1,458.28
B)$966.41
C)$979.21
D)$971.86
E)$977.96

Accepted Answer

To find the amount of each regular payment (PMT) to provide a future value (FV) of $14,000 in 10 years at an annual interest rate (r) of 8%, compounded annually, we use the future value of an annuity formula: $FV = PMT \times \frac{(1 + r)^n - 1}{r}$, where $n$ is the number of periods (years in this case), $r$ is the annual interest rate as a decimal, and $PMT$ is the payment amount per period. Rearranging the formula to solve for PMT gives us: $PMT = FV \times \frac{r}{(1 + r)^n - 1}$. Plugging in the values: $PMT = 14000 \times \frac{0.08}{(1 + 0.08)^{10} - 1}$, calculating this gives us approximately $966.41, which matches option B.

Question 19

Amy contributed $160 per month for 16 years to an account that paid 4% for the first 8 years, but 4.7% for the last 8 years.How much has she saved?
A)$44,896.93
B)$44,906.94
C)$44,908.93
D)$43,662.37

Accepted Answer

The correct answer is A.The amount saved in the first 8 years is $160 * 12 * 8 * 1.04 = $15,360.The amount saved in the last 8 years is $160 * 12 * 8 * 1.047 = $29,536.93.The total amount saved is $15,360 + $29,536.93 = $44,896.93.

Question 20

Find the amount of each regular payment to provide $5,000 in 5 years, at an annual rate r = 4%, compounded quarterly.
A)$241.08
B)$214.98
C)$227.08
D)$234.08
E)$242.63

Accepted Answer

To find the regular payment amount, we use the future value of an annuity formula: FV = Pmt * [(1 + r/n)^(nt) - 1] / (r/n). Here, FV = $5,000, r = 0.04, n = 4 (quarterly), and t = 5. Solving for Pmt gives approximately $227.08.

Quiz 9: Natural Number Functions and Probability

Find the amount of each regular payment to provide $22,000 in 15 years, at an annual rate r = 8%, compounded monthly.

Jim will retire in 30 years.He will invest $200 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 11%, Compounded monthly.Round to the nearest dollar.

Find the present value of an annuity with semiannual payments of $330 at 4.91%, compounded semiannually for 12 years.Round to the nearest cent.

Bank One offers a passbook account with a 3.6% annual rate, compounded quarterly.Bank Two offers a money market account at 3%, compounded monthly.Find the better growth by calculating the Effective rates.What is the greater effective rate?

Assume that $1,200 is deposited in an account in which interest is compounded annually at a rate of 5%.Find the accumulated amount after 10 years rounded to the nearest cent.

Assume that $150 is deposited at the end of each year into an account in which interest is compounded annually at a rate of 7.5%.Find the accumulated amount after 12 years.Round to the nearest cent.

Assume that $400 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 5 years.Round to the nearest cent.

A woman contributed $340\$ 340$340 per quarter for the first 12 years of an annuity, but changed to quarterly payments of $1,550\$ 1,550$1,550 for the last 12 years. Assuming 934%9 \frac { 3 } { 4 } \%943​% annual interest compounded quarterly, what is her accumulated value?

Find the periodic payment required to repay $12,330 over 15 years, with monthly payments at a 11% annual rate.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 5 years.Round to the nearest cent.

Find the periodic payment required to repay $1,870 repaid in 15 monthly installments, at an annual rate of 17%.Round to the nearest cent.

The Jepsens are buying a $24,900 car and financing it over the next 2 years.They secure a 5.7% loan. What will be the total of the monthly payments? Round to the nearest cent.

Assume that $150 is deposited at the end of each year in an account in which interest is compounded annually at a rate of 6%.Find the accumulated amount after 13 years.Round 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.

Find the effective interest rate given an annual rate of 7% and a compounding frequency of 6.Round your answer to two decimal places.

Which of these 20-year plans is best? All are at 8% annually. Plan A: $960\$ 960$960 each year for 10 years, and then let the accumulated amount grow for 10 years. Plan B: One payment of $7,680\$ 7,680$7,680 now, and let it grow.

Find the amount of each regular payment to provide $14,000 in 10 years, at an annual rate r = 8%, compounded annually.

Amy contributed $160 per month for 16 years to an account that paid 4% for the first 8 years, but 4.7% for the last 8 years.How much has she saved?

Find the amount of each regular payment to provide $5,000 in 5 years, at an annual rate r = 4%, compounded quarterly.

A woman contributed $\$ 340$ per quarter for the first 12 years of an annuity, but changed to quarterly payments of $\$ 1,550$ for the last 12 years. Assuming $9 \frac { 3 } { 4 } \%$ annual interest compounded quarterly, what is her accumulated value?

Which of these 20-year plans is best? All are at 8% annually. Plan A: $\$ 960$ each year for 10 years, and then let the accumulated amount grow for 10 years. Plan B: One payment of $\$ 7,680$ now, and let it grow.