Question 1

Solve the problem.
-Barbara knows that she will need to buy a new car in 5 years. The car will cost $15,000 by then. How much should she invest now at 5%, compounded quarterly, so that she will have enough to Buy a new car?
A) $11,193.23
B) $11,700.13
C) $13,257.81
D) $12,340.54

Accepted Answer

The answer of Solve the problem.
-Barbara knows that she will...

Question 2

Solve the problem.
-You have a choice of two accounts in which to invest your money for one year. Account A pays 4.6% simple interest rate and account B pays 3.5% interest compounded daily. Compute the Effective annual yield of account B and determine which account has the better rate. (Assume that There are 360 days in a year.)
A) There is not enough information to decide.
B) The rates are the same.
C) Account B
D) Account A

Accepted Answer

The answer of Solve the problem.
-You have a choice of...

Question 3

Solve the problem.
-How much money should you invest now to have $15,000 in 9 years if you invest the money at a Rate of 1.2%, compounded monthly?
A) $13,465.14
B) $14,211.87
C) $15,000.00
D) $14,865.67

Accepted Answer

To find the present value (the amount you should invest now) to have $15,000 in 9 years at an annual interest rate of 1.2% compounded monthly, you can use the formula for the present value of a single future amount: $PV = \frac{FV}{(1 + r/n)^{nt}}$, where PV is the present value, FV is the future value ($15,000), r is the annual interest rate (1.2% or 0.012 as a decimal), n is the number of times the interest is compounded per year (12 for monthly), and t is the time in years (9). Plugging in the values: $PV = \frac{15,000}{(1 + 0.012/12)^{12*9}}$, calculating this gives approximately $13,465.14.

Question 4

Solve the problem.
-John Leeʹs savings account has a balance of $3662. After 3 years, what will the amount of interest Be at 2% compounded semiannually?
A) $225.29
B) $224.14
C) $219.72
D) $110.96

Accepted Answer

The amount of interest can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), 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), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. In this case, P = $3662, r = 2% or 0.02, n = 2 (since the interest is compounded semiannually), and t = 3 years. Plugging these values into the formula gives A = 3662(1 + 0.02/2)^(2*3) = 3662(1 + 0.01)^6 ≈ 3662 * 1.061677812 = $3887.29. The amount of interest earned is then $3887.29 - $3662 = $225.29.

Question 5

Use an annual percentage rate table to solve the problem.

-In order to make some home improvements, a home owner spent $20,000. He paid 15% as a down Payment and financed the balance of the purchase with a 36-month fixed installment loan with an APR of 4.5%. Determine the home ownerʹs total finance charge and monthly payment.
A) Total finance charge = $1006.40; Monthly payment = $500.18
B) Total finance charge = $1205.30; Monthly payment = $505.70
C) Total finance charge = $2562.00; Monthly payment = $626.72
D) Total finance charge = $2920.60; Monthly payment = $553.35

Accepted Answer

The answer of Use an annual percentage rate table to...

Question 6

Solve the problem.
-The average cost of a 4-year college education is projected to be $100,000 in 15 years. How much Money should be invested now at 3.5%, compounded quarterly, to provide $100,000 in 15 years?
A) $59,290.78
B) $35,153.96
C) $100,000.00
D) $87,749.93

Accepted Answer

To find the present value (the amount that should be invested now) to achieve a future value of $100,000 in 15 years at an interest rate of 3.5% compounded quarterly, we use the formula for the present value of a single sum: $PV = \frac{FV}{(1 + r)^n}$, where FV is the future value, r is the interest rate per period, and n is the total number of periods. Here, r = 3.5%/4 = 0.875% per quarter, and n = 15 years * 4 quarters/year = 60 quarters. Plugging these values into the formula gives the present value required to reach $100,000 in 15 years, which matches choice A.

Question 7

Solve the problem.
-Andrea Gilfordʹs savings account has a balance of $453. After 2 years, what will the amount of Interest be at 4% compounded quarterly?
A) $37.53
B) $9.06
C) $28.53
D) $42.53

Accepted Answer

The interest can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount ($453), r is the annual interest rate (4%, or 0.04), n is the number of times that interest is compounded per year (quarterly, so n=4), and t is the time the money is invested for (2 years). Plugging in the values: A = 453(1 + 0.04/4)^(4*2) = 453(1 + 0.01)^8 ≈ 490.53. The interest earned is the final amount minus the principal: 490.53 - 453 = $37.53.

Question 8

Use an annual percentage rate table to solve the problem.
-A restaurant owner purchased a new dishwasher for $4000. She paid 15% down and financed the Balance with a 12-month fixed installment loan with an APR of 8.5%. Determine the total finance Charge and monthly payment for the loan.
A) Total finance charge = $261.46; Monthly payment = $305.12
B) Total finance charge = $167.96 ; Monthly payment = $297.33
C) Total finance charge = $158.44; Monthly payment = $296.54
D) Total finance charge = $208.80; Monthly payment = $350.73

Accepted Answer

The down payment is 15% of $4000, which is $600. The financed amount is $3400. Using an APR table or formula for a 12-month loan at 8.5%, the total finance charge is approximately $158.44, and the monthly payment is approximately $296.54.

Question 9

Solve the problem.
-Suppose you saw an advertisement in the newspaper for a financial planner who was Recommending a certificate of deposit that paid 5.5% interest compounded quarterly. In the fine Print at the bottom of the advertisement, it stated that the APY on the CD was 5.61%. Was this Advertisement accurate?
A) Yes
B) No

Accepted Answer

The advertisement is accurate because the APY (Annual Percentage Yield) takes into account the effect of compounding interest, which in this case is quarterly. The APY is slightly higher than the nominal interest rate of 5.5% due to compounding, making the advertisement's claim of a 5.61% APY correct and accurate.

Question 10

Solve the problem.
-Kerry invests $553 in a savings account that earns 3.4% compounded annually. Andy invests $553 In a savings account that earns 5% compounded annually. How much is in each of their accounts After 10 years and after 20 years? 
A) Kerry: $\$ 772.56 ; \$ 1079.28$
Andy: $\$ 900.78 ; \$ 1467.27$

B) Kerry: $\$ 747.15 ; \$ 1043.80$
Andy: $\$ 857.88 ; \$ 1397.40$

C) Kerry: $\$825.98; \$825.98$
Andy: $\$ 993.11 ; \$ 993.11$

D) Kerry: $\$ 722.59$; $\$ 944.18$
Andy: $\$817.03; \$1207.13$

Accepted Answer

To calculate the future value of investments compounded annually, use the formula $A = P(1 + r)^n$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (decimal), and $n$ is the time the money is invested for in years. For Kerry: $A = 553(1 + 0.034)^{10}$ and $A = 553(1 + 0.034)^{20}$. For Andy: $A = 553(1 + 0.05)^{10}$ and $A = 553(1 + 0.05)^{20}$. Calculating these gives the amounts for Kerry and Andy as in option A.

Question 11

Solve the problem.
-A small company borrows $30,000 at 4% compounded monthly. The loan is due in 6 years. How Much interest will the company pay?
A) $7995.60
B) $8092.04
C) $8122.26
D) $38,122.26

Accepted Answer

The interest paid can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount on maturity, P is the principal amount ($30,000), r is the annual interest rate (4% or 0.04), n is the number of times the interest is compounded per year (12, since it's compounded monthly), and t is the time the money is borrowed for in years (6). First, calculate the amount on maturity: A = 30000(1 + 0.04/12)^(12*6) = $38,122.26. The interest paid is then A - P = $38,122.26 - $30,000 = $8,122.26.

Question 12

Solve the problem.
-How much money should you invest now to have $5000 in 12 years if you invest the money at a Rate of 1.4%, compounded semiannually?
A) $2500.00
B) $4598.50
C) $4229.24
D) $3577.30

Accepted Answer

To find the present value (the amount you should invest now) to have $5000 in 12 years at a rate of 1.4% compounded semiannually, you use the formula for the present value of a single sum: $PV = \frac{FV}{(1 + r/n)^{nt}}$, where PV is the present value, FV is the future value ($5000), r is the annual interest rate (1.4% or 0.014), n is the number of times the interest is compounded per year (2 for semiannually), and t is the time in years (12). Plugging in the values: $PV = \frac{5000}{(1 + 0.014/2)^{2*12}}$, which calculates to approximately $4229.24.

Question 13

Use an annual percentage rate table to solve the problem.

-A cattle rancher needs to construct a new silo in which to store cattle feed. The silo will cost $2000. The rancher pays 15% as a down payment and finances the balance for 60 months at an APR of 7.50%. Determine the rancherʹs total finance charge and monthly payment.
A) Total finance charge = $368.22; Monthly payment = $34.47
B) Total finance charge = $343.91; Monthly payment = $34.07
C) Total finance charge = $273.02; Monthly payment = $32.88
D) Total finance charge = $404.60 ; Monthly payment = $40.08

Accepted Answer

The down payment is 15% of $2000, which is $300. The financed amount is $1700. Using the APR table for 7.50% over 60 months, the monthly payment is approximately $34.07, and the total finance charge is approximately $343.91.

Question 14

Solve the problem.
-Determine the effective annual yield for $1 invested for 1 year at 2.5% compounded quarterly.
A) 1.25%
B) -7.48%
C) 2.52%
D) 12.52%

Accepted Answer

The effective annual yield (EAY) can be calculated using the formula for compound interest: $EAY = (1 + \frac{r}{n})^n - 1$, where $r$ is the annual interest rate (expressed as a decimal) and $n$ is the number of compounding periods per year. For an annual interest rate of 2.5% or 0.025 compounded quarterly ($n = 4$), the calculation is $EAY = (1 + \frac{0.025}{4})^4 - 1$, which equals approximately 0.0252 or 2.52% when converted to a percentage.

Question 15

Solve the problem.
-Southwest Dry Cleaners believes that it will need new equipment in 6 years. The equipment will Cost $26,000. How much should be invested today at 2% compounded semiannually, to yield $26,000?
A) $24,548.93
B) $24,487.71
C) $25,169.60
D) $23,073.68

Accepted Answer

The answer of Solve the problem.
-Southwest Dry Cleaners believes that...

Question 16

Solve the problem.
-Determine the effective annual yield for $1 invested for 1 year at 4.5% compounded monthly.
A) 2.27%
B) 0.38%
C) 4.59%
D) -5.41%

Accepted Answer

The effective annual yield (EAY) can be calculated using the formula for compound interest: $EAY = (1 + \frac{r}{n})^n - 1$, where $r$ is the annual interest rate (expressed as a decimal) and $n$ is the number of compounding periods per year. For a 4.5% interest rate compounded monthly, $r = 0.045$ and $n = 12$. Plugging these values into the formula gives $EAY = (1 + \frac{0.045}{12})^{12} - 1 \approx 0.0459$ or 4.59%.

Question 17

Solve the problem.
-Sumi Katoʹs savings account has a balance of $624. After 14 years what will the amount of interest Be at 1.5% compounded annually?
A) $144.62
B) $133.62
C) $873.60
D) $150.62

Accepted Answer

The amount of interest can be found using the compound interest formula: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount ($624), r is the annual interest rate (1.5% or 0.015), n is the number of times that interest is compounded per year (1 for annually), and t is the time the money is invested for (14 years). Plugging in the values: A = 624(1 + 0.015/1)^(1*14) = 624(1.015)^14 ≈ $768.62. The interest earned is the final amount minus the principal: $768.62 - $624 = $144.62.

Question 18

Solve the problem.
-You have a choice of two accounts in which to invest your money for one year. Account A pays 3.1% simple interest rate and account B pays 2.5% interest compounded monthly. Compute the Effective annual yield of account B and determine which account has the better rate.
A) The rates are the same.
B) There is not enough information to decide.
C) Account A
D) Account B

Accepted Answer

The answer of Solve the problem.
-You have a choice of...

Question 19

Solve the problem.
-Determine the effective annual yield for $1 invested for 1 year at 3.5% compounded semiannually.
A) 3.53%
B) 3.55%
C) 3.5.00%
D) 3.56%

Accepted Answer

The effective annual yield (EAY) can be calculated using the formula for compound interest: $EAY = (1 + \frac{r}{n})^n - 1$, where $r$ is the annual interest rate (in decimal form) and $n$ is the number of compounding periods per year. For a 3.5% interest rate compounded semiannually, $r = 0.035$ and $n = 2$. Thus, $EAY = (1 + \frac{0.035}{2})^2 - 1 = (1.0175)^2 - 1 = 1.03530625 - 1 = 0.03530625$, or 3.53% when converted to a percentage.

Question 20

Solve the problem.
-How much money should you invest now in order to have $80,000 in 21 years? Assume that the Money earns interest at 2.6%, compounded annually?
A) $40,000.00
B) $27,220.80
C) $46,665.44
D) $9262.15

Accepted Answer

To find out how much money you should invest now to have $80,000 in 21 years at an annual interest rate of 2.6%, compounded annually, you can use the formula for the present value of a single future amount: $PV = \frac{FV}{(1 + r)^n}$, where PV is the present value (the amount you need to invest now), FV is the future value ($80,000), r is the annual interest rate (2.6% or 0.026 as a decimal), and n is the number of periods (21 years). Plugging in the values, we get: $PV = \frac{80,000}{(1 + 0.026)^{21}}$, which calculates to approximately $46,665.44.

Quiz 10: Consumer Mathematics

Solve the problem. -Barbara knows that she will need to buy a new car in 5 years. The car will cost $15,000 by then. How much should she invest now at 5%, compounded quarterly, so that she will have enough to Buy a new car?

Solve the problem. -How much money should you invest now to have $15,000 in 9 years if you invest the money at a Rate of 1.2%, compounded monthly?

Solve the problem. -John Leeʹs savings account has a balance of $3662. After 3 years, what will the amount of interest Be at 2% compounded semiannually?

Solve the problem. -The average cost of a 4-year college education is projected to be $100,000 in 15 years. How much Money should be invested now at 3.5%, compounded quarterly, to provide $100,000 in 15 years?

Solve the problem. -Andrea Gilfordʹs savings account has a balance of $453. After 2 years, what will the amount of Interest be at 4% compounded quarterly?

Use an annual percentage rate table to solve the problem. -A restaurant owner purchased a new dishwasher for $4000. She paid 15% down and financed the Balance with a 12-month fixed installment loan with an APR of 8.5%. Determine the total finance Charge and monthly payment for the loan.

Solve the problem. -Kerry invests $553 in a savings account that earns 3.4% compounded annually. Andy invests $553 In a savings account that earns 5% compounded annually. How much is in each of their accounts After 10 years and after 20 years?

Solve the problem. -A small company borrows $30,000 at 4% compounded monthly. The loan is due in 6 years. How Much interest will the company pay?

Solve the problem. -How much money should you invest now to have $5000 in 12 years if you invest the money at a Rate of 1.4%, compounded semiannually?

Solve the problem. -Determine the effective annual yield for $1 invested for 1 year at 2.5% compounded quarterly.

Solve the problem. -Southwest Dry Cleaners believes that it will need new equipment in 6 years. The equipment will Cost $26,000. How much should be invested today at 2% compounded semiannually, to yield $26,000?

Solve the problem. -Determine the effective annual yield for $1 invested for 1 year at 4.5% compounded monthly.

Solve the problem. -Sumi Katoʹs savings account has a balance of $624. After 14 years what will the amount of interest Be at 1.5% compounded annually?

Solve the problem. -You have a choice of two accounts in which to invest your money for one year. Account A pays 3.1% simple interest rate and account B pays 2.5% interest compounded monthly. Compute the Effective annual yield of account B and determine which account has the better rate.

Solve the problem. -Determine the effective annual yield for $1 invested for 1 year at 3.5% compounded semiannually.

Solve the problem. -How much money should you invest now in order to have $80,000 in 21 years? Assume that the Money earns interest at 2.6%, compounded annually?