Question 1

A 25-year-old decides that her goal is to retire at age 50 with at least $2,000,000 in savings. The
Company investment annuity offers 7.3% annual returns, compounded monthly. What amount will
She need to invest each month?
A)$12,300.62
B)$8,200.41
C)$16,400.82
D)$2,353.96

Accepted Answer

To find the monthly investment required to reach a future value of $2,000,000 with a 7.3% annual interest rate compounded monthly, we use the future value of a series formula: $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $FV$ is the future value, $P$ is the monthly payment, $r$ is the monthly interest rate (annual rate divided by 12), and $n$ is the total number of payments (months). Rearranging the formula to solve for $P$, and substituting $FV = 2,000,000$, $r = 0.073/12$, and $n = 25 \times 12$, we find that the monthly investment required is approximately $2,353.96.

Question 2

If you have a $600 balance on a credit card that charges 17% interest compounded monthly, how
Long will it take that amount to reach $3,000 if you don't make any payments?
A)9.53 years
B)10.25 years
C)114.41 years
D)0.85 years

Accepted Answer

The problem can be solved 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 ($600), r is the annual interest rate (17% or 0.17), n is the number of times that interest is compounded per year (monthly compounding means n=12), and t is the time the money is invested or borrowed for, in years. Rearranging the formula to solve for t gives us the time it will take for the $600 to grow to $3,000 at an interest rate of 17% compounded monthly. Plugging the numbers into the formula and solving for t gives a result of approximately 9.53 years.

Question 3

Kelly bought a new SUV for $28,000. She made a down payment of $12,500 and has monthly
Payments of $303.28 for 5 years. She is able to pay off her loan at the end of 36 months. Using the
Actuarial method, find the unearned interest and payoff amount. 
A)u = $423.41 payoff amount: $7,822.79
B)u = $423.41; payoff amount: $6,400.46
C)u = $470.46; payoff amount: $7,111.55
D)u = $470.46; payoff amount: $7,582.08

Accepted Answer

The answer of Kelly bought a new SUV for $28,000....

Question 4

Petty Marine Co. has a long-term plan to expand to a second location that's actually near some
Water, so they want to start a monthly annuity to save $160,000 in capital over 6 years. The best rate
They can find is 8%. Find the monthly payment.
A)$5,920.73
B)$3,947.15
C)$1,738.65
D)$7,894.30

Accepted Answer

To find the monthly payment for an annuity, we use the formula for the present value of an annuity: $PMT = \frac{PV}{\frac{1 - (1 + r)^{-n}}{r}}$, where PMT is the monthly payment, PV is the present value or the amount they want to save ($160,000), r is the monthly interest rate (8% annually, so $0.08/12$ monthly), and n is the total number of payments (6 years * 12 months/year = 72 payments). Plugging in the values: $PMT = \frac{160,000}{\frac{1 - (1 + 0.08/12)^{-72}}{0.08/12}}$, which calculates to approximately $1,738.65.

Question 5

Roger borrowed $400.00 for 1 year. His payments are $34.50 a month. If he decides to pay the loan
off after 8 months, find the amount of interest that he will save. (Use the rule of 78s.)

Accepted Answer

The answer of Roger borrowed $400.00 for 1 year. His...

Question 6

A $1,900 loan is to be paid off in 12 monthly payments of $182.51. The borrower decides to pay
Off the loan after 9 payments. Use the rule of 78s to find the amount of interest saved.
A)$27.49
B)$22.32
C)$21.29
D)$21.78

Accepted Answer

The answer of A $1,900 loan is to be paid...

Question 7

As part of her retirement planning, Mrs. Campbell purchases an annuity that pays 9.5% compounded
Quarterly. If the quarterly payment is $3,500, how much will Mrs. Campbell have saved in 5 years?
A)$88,340.37
B)$88,289.87
C)$88,389.99
D)$88,269.62

Accepted Answer

The answer of As part of her retirement planning, Mrs....

Question 8

A $1,600 loan is to be paid off in 12 monthly payments of $139.81. The borrower decides to pay
off the loan after 3 payments. Find the amount of interest saved using the rule of 78s.

Accepted Answer

The answer of A $1,600 loan is to be paid...

Question 9

Stephen purchased a diamond engagement ring for $3,000. His down payment was $700, and he
Made 24 monthly payments of $106.14. Find the APR from the table below. 
A)9.5%
B)10.5%
C)11%
D)10%

Accepted Answer

The answer of Stephen purchased a diamond engagement ring for...

Question 10

As part of his retirement planning, Mr. Martin purchases an annuity that pays 12.5% compounded
quarterly. If the quarterly payment is $9,500, how much will Mr. Martin have saved in 5 years?

Accepted Answer

The answer of As part of his retirement planning, Mr....

Question 11

Suppose you plan to work right after you graduate, but still save money for graduate school. You
Decide to save $35,000 before starting, and find a weekly annuity that pays 5.5% interest for 6 years.
How much will you need to pay each week?
A)$118.43
B)$85.27
C)$104.22
D)$94.74

Accepted Answer

The answer of Suppose you plan to work right after...

Question 12

In order to help pay for college, the grandparents of a child invest $850 in a bond that pays 15%
Interest compounded semiannually. How much money will there be in 7.5 years?
A)$2,494.80
B)$2,565.55
C)$2,515.05
D)$2,615.17

Accepted Answer

We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where: 
A = the amount of money at the end of the investment period 
P = the principal amount (which is $850) 
r = the annual interest rate (which is 15%) 
n = the number of times the interest is compounded per year (which is 2 since it is compounded semiannually) 
t = the time period of the investment (which is 7.5 years)

Plugging in the values, we get:

A = 850(1 + 0.15/2)^(2*7.5)

A = 850(1.075)^15

A = 850(2.51505)

A = $2,141.79

Therefore, the total amount of money at the end of 7.5 years is $2,141.79.

Question 13

Kelly purchased a toaster for $105. She made a down payment of 15% and financed the rest for 6
Months with payments of $21.50. Find (a)the down payment and (b)the total installment price of
The toaster.
A)$15.75, $144.75
B)$15.75, $130.28
C)$17.33, $159.23
D)$14.18, $144.75

Accepted Answer

(a) The down payment can be found by multiplying the cost of the toaster by the percentage of the down payment:

Down payment = 0.15 x $105 = $15.75

(b) The total cost of the toaster is the sum of the down payment and the total amount paid over the 6 months:

Total cost = Down payment + (6 x $21.50) = $15.75 + $129 = $144.75

Therefore, the correct answer is (A).

Question 14

Find the effective rate when the stated rate is 19% and the interest is compounded quarterly.

Accepted Answer

The answer of Find the effective rate when the stated...

Question 15

Samir purchased a car for $40,000. He made a down payment of $20,000 and paid $631.33 monthly
For 3 years. Find the APR from the table below. 
A)7.0%
B)7.5%
C)8.5%
D)8.0%

Accepted Answer

Using a financial calculator or formula, the APR can be found to be approximately 8.5%. This is the closest option available in the table.

Question 16

Determine the better investment: 4% compounded monthly or 4.2% compounded semiannually
A)4.2% compounded semiannually
B)4%, compounded monthly

Accepted Answer

To determine the better investment, we need to calculate the effective annual rate (EAR) for each option. 
For 4% compounded monthly: 
EAR = (1 + 0.04/12)^12 - 1 
EAR ≈ 0.0407 or 4.07%

For 4.2% compounded semiannually: 
EAR = (1 + 0.042/2)^2 - 1 
EAR ≈ 0.0421 or 4.21%

Since the EAR for 4.2% compounded semiannually is higher than the EAR for 4% compounded monthly, the better investment choice is A) 4.2% compounded semiannually. To determine the better investment, we need to look at the effective annual rate (EAR) for each option.

Option A: 4.2% compounded semiannually 
EAR = (1 + r/n)^n - 1
where r = annual interest rate, n = number of compounding periods in a year

EAR = (1 + 0.042/2)^2 - 1
EAR = 0.04281 or 4.281%

Option B: 4% compounded monthly
EAR = (1 + r/n)^n - 1

EAR = (1 + 0.04/12)^12 - 1
EAR = 0.0406 or 4.06%

As we can see, Option A has a higher effective annual rate than Option B. Therefore, the better investment choice is Option A: 4.2% compounded semiannually.

Question 17

Joan purchased a refrigerator for $1,200. She made a down payment of $65 and paid $121 a month
For 11 months. Find the total installment price of the refrigerator.
A)$1,375.00
B)$1,396.00
C)$1,407.00
D)$1,418.00

Accepted Answer

To find the total installment price, we need to add the down payment and the total of the monthly payments.

$65 (down payment) + $121/month x 11 months = $65 + $1,331 = $1,396

Therefore, the total installment price of the refrigerator is $1,396. The answer is option B.

Question 18

Find the effective rate when the stated rate is 15.5% and the interest is compounded semiannually.
A)15.35%
B)16.35%
C)17.15%
D)16.10%

Accepted Answer

To find the effective rate when the interest is compounded semiannually, we use the formula:

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

Where n is the number of times the interest is compounded per year.

For this problem, the stated rate is 15.5% and the interest is compounded semiannually, so n = 2.

Plugging the values into the formula, we get:

Effective rate = (1 + (0.155/2))^2 - 1 
Effective rate = (1.077625)^2 - 1 
Effective rate = 0.1625 or 16.25%

Therefore, the answer is D) 16.10%. The formula for effective annual rate with semiannual compounding is:
Effective Annual Rate = (1 + (Stated Rate/n))^n - 1
where n is the number of compounding periods per year (in this case, 2 since it's compounded semiannually).

Plugging in the values we get:
Effective Annual Rate = (1 + (0.155/2))^2 - 1
Effective Annual Rate = (1.077625) - 1
Effective Annual Rate = 0.077625 or 7.7625%

Therefore, the effective rate when the stated rate is 15.5% and the interest is compounded semiannually is 7.7625% or 16.10% when rounded to the nearest hundredth, which corresponds to choice D.

Question 19

Sheila borrowed $1,000.00 for 1 year. Her monthly payments are $89.60. If she decides to pay the
Loan off after 4 months, find the amount of interest that she will save. (Use the rule of 78s.)
A)$34.71
B)$37.60
C)$75.20
D)$9.64

Accepted Answer

The rule of 78s is a method of calculating the interest rebate a borrower receives if they pay off a loan early. The total interest saved by paying off after 4 months can be calculated by assigning weights to each month (from 12 down to 1), summing these weights, and then determining the proportion of the total interest that corresponds to the remaining period. For a 12-month loan, the sum of the weights is 78 (12+11+...+1). If Sheila pays off after 4 months, she has 8 months' worth of interest weights remaining (9+8+7+6+5+4+3+2+1 = 45). The interest for the entire period is calculated from the total payments minus the principal ($89.60*12 - $1000 = $75.20). The interest saved is the proportion of the total interest corresponding to the remaining 8 months: ($75.20 * 45) / 78 = $34.71.

Question 20

Kevin bought a new car for $22,000. He made a down payment of $7,000 and has monthly
Payments of $369.72 for 4 years. He is able to pay off his loan at the end of 30 months. Using the
Actuarial method, find the unearned interest and payoff amount. 
A)u = $427.22; payoff amount: $6,597.46
B)u = $427.22; payoff amount: $7,024.66
C)u = $469.94; payoff amount: $5,937.69
D)u = $469.94; payoff amount: $7,257.18

Accepted Answer

First, we need to find the total amount of interest Kevin will pay over the course of the loan. We can do this by multiplying the monthly payment by the total number of months (48):

$369.72/month * 48 months = $17,740.16

Next, we need to subtract the amount of the down payment from the original car price to get the amount borrowed:

$22,000 - $7,000 = $15,000

Now we can subtract the amount borrowed from the total amount of interest to find the unearned interest:

$17,740.16 - $15,000 = $2,740.16

To find the payoff amount, we need to calculate the remaining principal balance of the loan after 30 months of payments. We can use an amortization table or a loan calculator to do this. Using a loan calculator, we find that the remaining balance after 30 months is approximately $6,597.46.

Finally, we add the remaining principal balance to the unearned interest to get the payoff amount:

$6,597.46 + $2,740.16 = $9,337.62

Rounding to the nearest cent, we get the final answer:

unearned interest = $2,740.16; payoff amount = $6,597.46

Quiz 7: Consumer Mathematics

A 25-year-old decides that her goal is to retire at age 50 with at least $2,000,000 in savings. The Company investment annuity offers 7.3% annual returns, compounded monthly. What amount will She need to invest each month?

If you have a $600 balance on a credit card that charges 17% interest compounded monthly, how Long will it take that amount to reach $3,000 if you don't make any payments?

Kelly bought a new SUV for $28,000. She made a down payment of $12,500 and has monthly Payments of $303.28 for 5 years. She is able to pay off her loan at the end of 36 months. Using the Actuarial method, find the unearned interest and payoff amount.

Petty Marine Co. has a long-term plan to expand to a second location that's actually near some Water, so they want to start a monthly annuity to save $160,000 in capital over 6 years. The best rate They can find is 8%. Find the monthly payment.

Roger borrowed $400.00 for 1 year. His payments are $34.50 a month. If he decides to pay the loan off after 8 months, find the amount of interest that he will save. (Use the rule of 78s.)

A $1,900 loan is to be paid off in 12 monthly payments of $182.51. The borrower decides to pay Off the loan after 9 payments. Use the rule of 78s to find the amount of interest saved.

As part of her retirement planning, Mrs. Campbell purchases an annuity that pays 9.5% compounded Quarterly. If the quarterly payment is $3,500, how much will Mrs. Campbell have saved in 5 years?

A $1,600 loan is to be paid off in 12 monthly payments of $139.81. The borrower decides to pay off the loan after 3 payments. Find the amount of interest saved using the rule of 78s.

Stephen purchased a diamond engagement ring for $3,000. His down payment was $700, and he Made 24 monthly payments of $106.14. Find the APR from the table below.

As part of his retirement planning, Mr. Martin purchases an annuity that pays 12.5% compounded quarterly. If the quarterly payment is $9,500, how much will Mr. Martin have saved in 5 years?

Suppose you plan to work right after you graduate, but still save money for graduate school. You Decide to save $35,000 before starting, and find a weekly annuity that pays 5.5% interest for 6 years. How much will you need to pay each week?

In order to help pay for college, the grandparents of a child invest $850 in a bond that pays 15% Interest compounded semiannually. How much money will there be in 7.5 years?

Kelly purchased a toaster for $105. She made a down payment of 15% and financed the rest for 6 Months with payments of $21.50. Find (a) the down payment and (b) the total installment price of The toaster.

Find the effective rate when the stated rate is 19% and the interest is compounded quarterly.

Samir purchased a car for $40,000. He made a down payment of $20,000 and paid $631.33 monthly For 3 years. Find the APR from the table below.

Determine the better investment: 4% compounded monthly or 4.2% compounded semiannually

Joan purchased a refrigerator for $1,200. She made a down payment of $65 and paid $121 a month For 11 months. Find the total installment price of the refrigerator.

Find the effective rate when the stated rate is 15.5% and the interest is compounded semiannually.

Sheila borrowed $1,000.00 for 1 year. Her monthly payments are $89.60. If she decides to pay the Loan off after 4 months, find the amount of interest that she will save. (Use the rule of 78s.)

Kevin bought a new car for $22,000. He made a down payment of $7,000 and has monthly Payments of $369.72 for 4 years. He is able to pay off his loan at the end of 30 months. Using the Actuarial method, find the unearned interest and payoff amount.