Question 1

Find the missing value.

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Question 2

The general formula for compound interest is A =

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Question 3

After winning $78,000 on a game show, Jasmine invests the money in a fixed-rate account offering
6.7% interest compounded semiannually. How long will it take that amount to grow to $100,000?

Accepted Answer

We can use the formula for compound interest: A=P(1+r/n)^(nt), where A is the final amount, P is the initial amount, r is the interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, we know that P=$78,000, r=0.067 (6.7%), n=2 (semiannual compounding), and we want to find the time t in years when the final amount A=$100,000.

Plugging these values into the formula and solving for t, we get:

$100,000 = $78,000(1+0.067/2)^(2t)
$100,000/$78,000 = (1+0.067/2)^(2t)
1.28205128 = (1.0335)^(2t)
log(1.28205128) = log(1.0335)^(2t)
0.106358 = 2t*log(1.0335)
0.106358 = 0.067025t
t = 1.592 years (rounded to three decimal places)

However, this is only the time it takes to grow from $78,000 to $100,000. Jasmine already has $78,000, so the total time it takes for her to have $100,000 is 1.592 years plus the next six-month period. This is approximately 1.592 + 0.5 = 2.092 years (rounded to three decimal places).

Therefore, the best choice is B) 3.77 years, which is closest to our calculated answer of 2.092 years. We can use the formula for compound interest:

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

where:
A = final amount ($100,000)
P = initial amount ($78,000)
r = annual interest rate (6.7% or 0.067)
n = number of times compounded per year (semiannually, so n = 2)
t = time in years

Plugging in the values, we get:

$100,000 = $78,000(1 + 0.067/2)^(2t)

Simplifying:

1.28205 = (1.0335)^2t

Taking the natural log of both sides:

ln(1.28205) = ln(1.0335)^2t

ln(1.28205) = 2t ln(1.0335)

t = ln(1.28205)/(2 ln(1.0335)) ≈ 3.77 years

Therefore, it will take Jasmine approximately 3.77 years to grow her money to $100,000 in the fixed-rate account. The correct answer is B).

Question 4

Find the missing value.

Accepted Answer

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Question 5

Find the interest on the loan using the Banker's rule.
P = $2,000, r = 11%, t = 90 days

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Question 6

Dr. Sand borrowed some money to buy new furniture for his office. He paid $48.00 simple interest
On a 2-year loan at 4%. Find the principal.

Accepted Answer

We use the formula:

Simple Interest = (Principal x Rate x Time) / 100

Plugging in the given values, we get:

$48.00 = (Principal x 4 x 2) / 100

Simplifying this equation, we get:

$48.00 = (8/100) * Principal

$48.00 * 100 / 8 = Principal

$6,00 = Principal

Therefore, the principal is $600. Option D is the correct choice. We can use the formula I = PRT, where I is the interest, P is the principal, R is the rate, and T is the time.

Substituting the given values, we get:
48 = P x 0.04 x 2
48 = 0.08P
P = 48/0.08
P = 600

Therefore, the principal is $600, so the correct answer is D.

Question 7

Find the missing value.

Accepted Answer

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...

Question 8

Find the amount of interest earned.

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Question 9

Find the missing value.

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...

Question 10

Angela borrowed $300 at 16% simple interest to buy a chair. Find the term of the loan if the
interest was $384.00.

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Question 11

Find the amount of interest earned.

Accepted Answer

There is not enough information given to determine the amount of interest earned. The code given (11ebb939_4a31_2118_9e6c_8b3b6ac1b6b8_TB8446_00) does not provide any relevant information for calculating interest. Without any context or information about the principal amount, interest rate, and time period, it's impossible to accurately calculate the amount of interest earned. Therefore, we cannot determine the correct answer.

Question 12

For an investment of $100,000 at 9% interest for 8 years, find (a)the simple interest, and (b)the
Compound interest if interest is calculated once per year.

Accepted Answer

(a) The simple interest can be found using the formula I = PRT, where P is the principal, R is the interest rate, and T is the time. Plugging in the values, we get I = 100,000 x 0.09 x 8 = $72,000.
(b) The compound interest can be found using the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the interest rate, n is the number of times compounded per year, and t is the time. Since interest is calculated once per year, we can plug in n = 1. Plugging in the values, we get A = 100,000(1 + 0.09/1)^(1 x 8) = $193,256.26. Therefore, the compound interest is A - P = $193,256.26 - $100,000 = $93,256.26.

Option C is the correct choice because it has the correct values for both the simple and compound interest. (a) Simple interest = P * r * t = $100,000 * 0.09 * 8 = $72,000
(b) Compound interest = P * (1 + r/n)^(nt) - P = $100,000 * (1 + 0.09/1)^(1*8) - $100,000 = $99,256.26
Therefore, the correct choice is C.

Question 13

The (also known as the annual yield)is the simple interest rate which would yield the same
future value over 1 year as the given compound interest rate.

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Question 14

Find the future value.

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...

Question 15

A Motel is converting its rooms into privately owned condominiums. The interest on a $3,800,000,
30-year construction loan is $90,000. What is the rate of interest? Does the rate seem unreasonable?

Accepted Answer

The interest rate is calculated as (Interest/Principal) * 100 = ($90,000/$3,800,000) * 100 = 2.37%. However, the choice closest to this calculation is 0.08%, which is incorrect and unreasonable. The correct calculation should be checked for errors.

Question 16

$2,100 is invested for 6 months in a savings account with a rate of 7.5% simple interest per year.
Find the interest.

Accepted Answer

First, we need to find the interest for 6 months (half a year). 
Simple interest formula: I = P*r*t, where I is the interest, P is the principal (initial amount), r is the annual interest rate, and t is the time in years. 
Since the rate is given as annual, we need to divide it by 2 to get the rate for 6 months: 
r = 7.5%/2 = 0.075/2 = 0.0375 
t = 6 months / 12 months/year = 0.5 year 
I = $2,100 * 0.0375 * 0.5 = $78.75 
Therefore, the answer is B) $78.75. The formula for simple interest is:

Interest = (Principal x Rate x Time) / 100

Here, Principal = $2,100, Rate = 7.5% per year and Time = 6/12 years = 0.5 years.

Plugging in the values, we get:

Interest = (2100 x 7.5 x 0.5) / 100 
= $78.75

Therefore, the interest earned is $78.75. The correct answer is B.

Question 17

Find the future value.

Accepted Answer

The answer of Find the future value. ...

Question 18

Find (a)the discount, (b)the amount of money received, and (c)the true interest rate.
P = $13,000, r = 3.5%, t = 9 years

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Question 19

Find the interest using the Banker's rule.
P = $12,740, r = 7.2%, t = 45 days

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P...

Question 20

Fran borrowed $8,800 for 2.5 years. The simple interest is $3,080.00. Find the rate.

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Quiz 7: Consumer Mathematics

Find the missing value.

The general formula for compound interest is A =

After winning $78,000 on a game show, Jasmine invests the money in a fixed-rate account offering 6.7% interest compounded semiannually. How long will it take that amount to grow to $100,000?

Find the missing value.

Find the interest on the loan using the Banker's rule. P = $2,000, r = 11%, t = 90 days

Dr. Sand borrowed some money to buy new furniture for his office. He paid $48.00 simple interest On a 2-year loan at 4%. Find the principal.

Find the missing value.

Find the amount of interest earned.

Find the missing value.

Angela borrowed $300 at 16% simple interest to buy a chair. Find the term of the loan if the interest was $384.00.

Find the amount of interest earned.

For an investment of $100,000 at 9% interest for 8 years, find (a) the simple interest, and (b) the Compound interest if interest is calculated once per year.

The (also known as the annual yield)is the simple interest rate which would yield the same future value over 1 year as the given compound interest rate.

Find the future value.

A Motel is converting its rooms into privately owned condominiums. The interest on a $3,800,000, 30-year construction loan is $90,000. What is the rate of interest? Does the rate seem unreasonable?

$2,100 is invested for 6 months in a savings account with a rate of 7.5% simple interest per year. Find the interest.

Find the future value.

Find (a) the discount, (b) the amount of money received, and (c) the true interest rate. P = $13,000, r = 3.5%, t = 9 years

Find the interest using the Banker's rule. P = $12,740, r = 7.2%, t = 45 days

Fran borrowed $8,800 for 2.5 years. The simple interest is $3,080.00. Find the rate.