Audrey is buying a new car for $32,998.00. She plans to make a down payment of $4,200.00. If she's to make monthly payments of $525 for the next five years, what APR has she paid?A. 37%
B. .37%
C. 3%
D. 3.7%

Answers

Answer 1

Answer: This question is an annuity problem with cost of the car = $32,998, the present value of the annuity (PV) is given by the difference between the cost of the car and the down payment = $32,998 - $4,200 = $28,798. The monthly payments (P) = $525 and the number of number of years (n) = 5 years and the number of payments in a year (t) is 12 payments (i.e. monthly) The formula for the present value of an annuity is given by PV = (1 - (1 + r/t)^-nt) / (r/t) 28798 = 525(1 - (1 + r/12)^-(5 x 12)) / (r/12) 28798r / 12 = 525(1 - (1 + r/12)^-60) 28798r / (12 x 525) = 1 - (1 + r/12)^-60 2057r / 450 = 1 - (1 + r/12)^-60 Substituting option A (r = 37% = 0.37) 2057r / 450 = 2057(0.37) / 450 = 761.09 / 450 = 1.691 1 - (1 + r/12)^60 = 1 - (1 + 0.37/12)^-60 = 1 - 0.1617 = 0.8383 Therefore, r is not 37% Substituting option D (r = 3.7% = 0.037) 2057r / 450 = 2057(0.037) / 450 = 76.109 / 450 = 0.1691 1 - (1 + r/12)^60 = 1 - (1 + 0.037/12)^-60 = 1 - 0.8313 = 0.1687 Therefore, r is approximately 3.7%

Answer 2

Answer:

To solve this we are going to use the loan payment formula: $P= ( (r)/(n)(PV))/(1-(1+ (r)/(n))^(-nt) )$

where

$P$ is the amount of the regular payment

$PV$ is the present debt

$r$ is APR in decimal form

$n$ is the number of payments per year

$t$ is the time in years

We know from our problem that Audrey is making a down payment of $4,200.00; since the cost of the car is $32,998.00, the present deb will be the cost of the car minus the down payment, so $PV=32998-4200=28798$ . We also know that she is going to make monthly payments of $525 for the next five years, so $n=12$ and $t=12$ . Let's replace the values in our formula:

$P= ( (r)/(n)(PV))/(1-(1+ (r)/(n))^(-nt) )$

$525= ( (r)/(12)(28798))/(1-(1+ (r)/(12))^(-(12)(5)) )$

We have two ways of finding the APR: we can solve for $r$ in our equation, which is extremely difficult, or we can evaluate the given APRs and check for which one both sides of the equation are almost the same. Since the second is way easier, we are going to use it.

A. 37%

The APR should be in decimal form, so we need to convert it first; to do it we are going to divide the APR by 100%

$r=(37)/(100) =0.37$

Let's replace the ARP in decimal form in our equation

$525= ( (0.37)/(12)(28798))/(1-(1+ (0.37)/(12))^(-(12)(5)) )$

$525=1059.20$

$529\neq 1059.20$

Since 529 is not equal to 1059.20, 37% is not the APR of the loan.

B. .37%

- Convert the APR to decimal form

$r=(0.37)/(100) =0.0037$

- Replace the APR

$525= ( (0.0037)/(12)(28798))/(1-(1+ (0.0037)/(12))^(-(12)(5)) )$

$525=484.49$

Since 525 is not equal to 484.59, .37% is not the APR of the loan.

C. 3%

- Convert the APR to decimal form

$r=(3)/(100) =0.03$

- Replace the APR

$525= ( (0.03)/(12)(28798))/(1-(1+ (0.03)/(12))^(-(12)(5)) )$

$525=517.46$

Since 525 is not equal to 517.46, 3% is not the APR of the loan.

D. 3.7%

- Convert the APR to decimal form

$r=(3.7)/(100) =0.037$

- Replace the APR

$525= ( (0.037)/(12)(28798))/(1-(1+ (0.037)/(12))^(-(12)(5)) )$

$525=526.47$

Since 525 is almost equal to 526.47, 3.7% is the APR of the loan.

We can conclude that the correct answer is D. 3.7%

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2.The price of a gallon of gasoline is $3.60. The price when Ryan's mother started driving was 4 of the current price. What was
the price of gasoline when Ryan's mother started driving?
OA. $1.40
OB. $3.85
OC. $3.35
OD. $0.90

Answers

OD. $0.90

3.60/4 = price when Ryan’s mother started driving

3.6/4= $0.90

Answer:

OD. $0.90

3.60/4 = price when Ryan’s mother started driving

3.6/4= $0.90

Step-by-step explanation:

Brendon had total job benefits of $39,500 last year. He was required to wear a shirt with the company logo on it for work that he was responsible for buying. Brendon purchased 12 shirts for work during the year at a cost of $23.95 each. He was also required to attend a training at a cost to him of $135. What was Brendon’s total employment compensation last year? a. $39,077.60 b. $39,212.60 c. $39,341.05 d. $39,922.40

Answers

Answer:

a. $39,077.60

Step-by-step explanation:

We have been given that Brendon had total job benefits of $39,500 last year. Brendon purchased 12 shirts for work during the year at a cost of $23.95 each.

To find Brendon's total employment compensation, we will subtract total expenses from Brendon's total job benefits.

Let us find the cost of 12 shirts by multiplying $23.95 by 12.

$\text{Amount spent on 12 shirts}=12* \$23.95$

$\text{Amount spent on 12 shirts}=\$287.40$

To find the total expenses we will add the cost of training in cost of 12 shirts.

$\text{Brendon's total expenses}=\$287.40+\$135$

$\text{Brendon's total expenses}=\$422.40$

Let us subtract total expenses from total job benefits.

$\text{Brendon’s total employment compensation last year}=\$39,500-\$422.40$

$\text{Brendon’s total employment compensation last year}=\$39,077.60$

Therefore, Brendon’s total employment compensation last year was $39,077.60 and option 'a' is the correct choice.

39,500 - (12 * 23.95) - 135 = 39,077.60

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Answers

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Charlotte measured the temperature at 7:00 A.M. and again at 3:00 P.M. She placed both measurements on a number line.How did the temperature change between 7:00 A.M. and 3:00 P.M.?

A.
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B.
It decreased by °C.

C.
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D.
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Answers

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Step-by-step explanation:

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Audrey is buying a new car for $32,998.00. She plans to make a down payment of $4,200.00. If she's to make monthly payments of $525 for the next five years, what APR has she paid?A. 37% B. .37% C. 3% D. 3.7%

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Audrey is buying a new car for $32,998.00. She plans to make a down payment of $4,200.00. If she's to make monthly payments of $525 for the next five years, what APR has she paid?A. 37%
B. .37%
C. 3%
D. 3.7%