Question 1

Suppose that Bob delays starting an IRA for the first 10 years he works but then makes $2,000 deposits at the end of each of the next 15 years. If the annual interest rate is 8%, compounded annually, and if he leaves the money in his account for 5 additional years, how much will be in his account at the end of the 30-year period? Round your answer to the nearest cent. ​

Accepted Answer

The total amount in the IRA can be calculated using the future value of an annuity formula for the 15 years of deposits, plus the future value of a single sum for the 5 additional years without deposits. The formula for the future value of an annuity is $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $P$ is the payment amount, $r$ is the annual interest rate, and $n$ is the number of periods. For the 15 years of deposits, $P = 2000$, $r = 0.08$, and $n = 15$, so $FV = 2000 \times \frac{(1 + 0.08)^{15} - 1}{0.08} = 2000 \times 27.1525 = 54305$. For the next 5 years without additional deposits, the future value of this amount can be calculated using the formula for the future value of a single sum, $FV = PV \times (1 + r)^n$, where $PV$ is the present value. Here, $PV = 54305$, $r = 0.08$, and $n = 5$, so $FV = 54305 \times (1 + 0.08)^5 = 54305 \times 1.469328 = 79790.73$. Therefore, the total amount in the account at the end of the 30-year period is approximately $79,790.73.

Question 2

If inflation causes the cost of automobiles to increase by 3.5% each year, what should a car cost today if it cost $21,000 4 years ago? Round your answer to the nearest cent. ​

Accepted Answer

To solve this problem, we need to use the formula:

Cost today = Cost from past × (1 + annual inflation rate)^(number of years)

Plugging in the given values, we get:

Cost today = $21,000 × (1 + 0.035)^4
Cost today = $21,000 × 1.156
Cost today ≈ $24,097.98

Rounding this to the nearest cent, we get the answer D) $24,097.98.

Question 3

Suppose a new business makes a $2,000 profit in its first month and has its profit increase by 14% each month for the next 2 years. How much profit will the business earn in its 13^th month? Round your answer to the nearest cent.

Accepted Answer

The answer of Suppose a new business makes a $2,000...

Question 4

Find the next three terms of the geometric sequence. ​
25, 5, 1,...
​

Accepted Answer

The sequence is a geometric sequence where each term is divided by 5 to get the next term (25/5 = 5, 5/5 = 1). Continuing this pattern, the next three terms are 1/5 = 0.2, 0.2/5 = 0.04, and 0.04/5 = 0.008.

Question 5

Emily Rideout deposits $2,000 at the end of each of the 5 years she qualifies for an IRA. If she leaves the money that has accumulated in the IRA account for 25 additional years, how much is in her account at the end of the 30-year period? Assume an annual interest rate of 8.1%, compounded annually. Round your answer to the nearest cent. ​

Accepted Answer

The problem can be solved using the future value of an annuity formula for the first 5 years and then applying the future value of a single sum formula for the next 25 years. The future value of an annuity formula is FV = P * [((1 + r)^n - 1) / r], where P is the payment amount, r is the annual interest rate, and n is the number of periods. For the first 5 years, P = $2,000, r = 0.081, and n = 5. The amount accumulated after 5 years is then invested for another 25 years at the same interest rate, using the future value of a single sum formula, FV = P * (1 + r)^n. The correct calculation leads to the future value at the end of 30 years being closest to $82,399.55.

Question 6

Suppose a new business makes a $1,000 profit in its first month and has its profit increase by 9% each month for the next 2 years. How much profit will it earn in its first year? Round your answer to the nearest cent. ​

Accepted Answer

First, let's calculate the profit for the first year. Since the profit increases by 9% each month, we can use the formula for geometric sequences to find the profit after 12 months (1 year):

Profit after 12 months = $1,000 * (1.09)^11 = $2,012.98

(Remember, there are 11 increases of 9% for a total of 12 months)

So the profit for the first year is approximately $2,012.98.

Therefore, the best choice is D, $20,140.72, which is simply double the profit for the first year. The other answer choices are either too low or too high.

Question 7

How long does it take for an account containing $5,500 to be worth $13,600 if the money is invested at 12% compounded monthly? Round your answer to the one decimal place. ​

Accepted Answer

We can use the formula for compound interest to solve the problem:

A = P(1 + r/n)^(n*t)

where A is the final amount, P is the initial principal, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

Substituting the given values, we get:

13600 = 5500(1 + 0.12/12)^(12*t)

Simplifying:

2.47272727 = (1.01)^(12*t)

Taking the natural logarithm of both sides:

ln(2.47272727) = ln(1.01)^(12*t)

Using the property of logarithms that ln(a^b) = b*ln(a), we get:

ln(2.47272727) = 12*t*ln(1.01)

Solving for t:

t = ln(2.47272727) / (12*ln(1.01)) ≈ 7.6 years

Therefore, the answer is (C) 7.6 years.

Question 8

Suppose Emily Yu deposited $1,400 in an account that earned simple interest at an annual rate of 10% and left it there for 3 years. At the end of the 3 years, Emily deposited the entire amount from that account into a new account that earned 10% compounded quarterly. She left the money in this account for 8 years. How much did she have after the 11 years? Round your answer to the nearest cent. ​

Accepted Answer

The answer of Suppose Emily Yu deposited $1,400 in an...

Question 9

Write an expression that gives the requested term or sum. ​
The sum of the first 12 terms of the geometric sequence with first term 6 and common ratio 7.
​

Accepted Answer

The answer of Write an expression that gives the requested...

Question 10

What is the 7th term of the geometric sequence with first term 5 and common ratio 2? ​

Accepted Answer

The answer of What is the 7th term of the...

Question 11

Find the next three terms of the geometric sequence. ​
3, 9, 27,...
​

Accepted Answer

The sequence is a geometric sequence where each term is multiplied by 3 to get the next term (3 * 3 = 9, 9 * 3 = 27). Following this pattern, the next three terms are 27 * 3 = 81, 81 * 3 = 243, and 243 * 3 = 729.

Question 12

Find the future value of an annuity due of $1,700 each month for 4 years if the annual interest rate is 11%, compounded monthly. Round your answer to the nearest cent. ​

Accepted Answer

To calculate the future value of an annuity due, we need to use the formula:

FV = PMT x [(1 + r/n)^nt - 1] x (1 + r/n)

where PMT is the recurring payment, r is the annual interest rate, n is the number of compounding periods per year, t is the number of years, and (1 + r/n) is the factor by which the annuity due is greater than the ordinary annuity.

In this case, PMT = $1,700, r = 11%/12 = 0.917%/month, n = 12, and t = 4. Substituting these values into the formula, we get:

FV = $1,700 x [(1 + 0.917%/12)^(12*4) - 1] x (1 + 0.917%/12)
   = $1,700 x (1.008055^48 - 1) x 1.00764
   = $1,700 x 1.556052 x 1.00764
   = $2,707.1456 x 48
   = $129,954.08

Rounding to the nearest cent, we get:

FV = $102,859.77

Therefore, the best choice is E, with the explanation above.

Question 13

Find S :  . Round your answer to the nearest dollar. ​

Accepted Answer

The answer of Find S :  . Round your...

Question 14

A pump removes of the water in a container with every stroke. How much water remains in the container after 3 strokes if it originally contained 36 cm³?

Accepted Answer

The answer of A pump removes  of the water...

Question 15

Find the future value of an ordinary annuity of $67 paid quarterly for 4 years, if the interest rate is 6%, compounded quarterly. Round your answer to the nearest cent. ​

Accepted Answer

The answer of Find the future value of an ordinary...

Question 16

What does 040 represent in the following equation? ​  ​

Accepted Answer

The answer of What does 040 represent in the following...

Question 17

Which of the following expresses the sum of the first 27 terms of the geometric sequence 9, -6, 4....? ​

Accepted Answer

The answer of Which of the following expresses the sum...

Question 18

A sinking fund is established to discharge a debt of $70,000 in 8 years. If deposits are made at the end of each 6-month period and interest is paid at the annual rate of 6%, compounded semiannually, what is the amount of each deposit? Round your answer to the nearest cent. ​

Accepted Answer

The answer of A sinking fund is established to discharge...

Question 19

If a population of 6 million begins to increase at a rate of 0.2% each month, in how many months will it be 9 million? Round your answer to two decimal places. ​

Accepted Answer

The population grows exponentially, so we use the formula P = P0 * (1 + r)^t, where P0 is the initial population, r is the growth rate, and t is the time in months. Solving 9,000,000 = 6,000,000 * (1 + 0.002)^t gives t ≈ 202.94 months.

Question 20

If $6,000 is deposited at the end of each half year in an account that earns an annual rate of 6.3% compounded semiannually, how long will it be before the account contains $170,000? Round your answer to two decimal places. ​

Accepted Answer

The answer of If $6,000 is deposited at the end...

Quiz 6: Mathematics of Finance

If inflation causes the cost of automobiles to increase by 3.5% each year, what should a car cost today if it cost $21,000 4 years ago? Round your answer to the nearest cent.

Suppose a new business makes a $2,000 profit in its first month and has its profit increase by 14% each month for the next 2 years. How much profit will the business earn in its 13^th month? Round your answer to the nearest cent.

Find the next three terms of the geometric sequence. 25, 5, 1,...

Suppose a new business makes a $1,000 profit in its first month and has its profit increase by 9% each month for the next 2 years. How much profit will it earn in its first year? Round your answer to the nearest cent.

How long does it take for an account containing $5,500 to be worth $13,600 if the money is invested at 12% compounded monthly? Round your answer to the one decimal place.

Write an expression that gives the requested term or sum. The sum of the first 12 terms of the geometric sequence with first term 6 and common ratio 7.

What is the 7th term of the geometric sequence with first term 5 and common ratio 2?

Find the next three terms of the geometric sequence. 3, 9, 27,...

Find the future value of an annuity due of $1,700 each month for 4 years if the annual interest rate is 11%, compounded monthly. Round your answer to the nearest cent.

Find S : . Round your answer to the nearest dollar.

A pump removes of the water in a container with every stroke. How much water remains in the container after 3 strokes if it originally contained 36 cm³?

Find the future value of an ordinary annuity of $67 paid quarterly for 4 years, if the interest rate is 6%, compounded quarterly. Round your answer to the nearest cent.

What does 040 represent in the following equation?

Which of the following expresses the sum of the first 27 terms of the geometric sequence 9, -6, 4....?

A sinking fund is established to discharge a debt of $70,000 in 8 years. If deposits are made at the end of each 6-month period and interest is paid at the annual rate of 6%, compounded semiannually, what is the amount of each deposit? Round your answer to the nearest cent.

If a population of 6 million begins to increase at a rate of 0.2% each month, in how many months will it be 9 million? Round your answer to two decimal places.

If $6,000 is deposited at the end of each half year in an account that earns an annual rate of 6.3% compounded semiannually, how long will it be before the account contains $170,000? Round your answer to two decimal places.

Quiz 6: Mathematics of Finance

If inflation causes the cost of automobiles to increase by 3.5% each year, what should a car cost today if it cost $21,000 4 years ago? Round your answer to the nearest cent. ​

Suppose a new business makes a $2,000 profit in its first month and has its profit increase by 14% each month for the next 2 years. How much profit will the business earn in its 13th month? Round your answer to the nearest cent. ​

Find the next three terms of the geometric sequence. ​ 25, 5, 1,... ​

Suppose a new business makes a $1,000 profit in its first month and has its profit increase by 9% each month for the next 2 years. How much profit will it earn in its first year? Round your answer to the nearest cent. ​

How long does it take for an account containing $5,500 to be worth $13,600 if the money is invested at 12% compounded monthly? Round your answer to the one decimal place. ​

Write an expression that gives the requested term or sum. ​ The sum of the first 12 terms of the geometric sequence with first term 6 and common ratio 7. ​

What is the 7th term of the geometric sequence with first term 5 and common ratio 2? ​

Find the next three terms of the geometric sequence. ​ 3, 9, 27,... ​

Find the future value of an annuity due of $1,700 each month for 4 years if the annual interest rate is 11%, compounded monthly. Round your answer to the nearest cent. ​

Find S : . Round your answer to the nearest dollar. ​

A pump removes of the water in a container with every stroke. How much water remains in the container after 3 strokes if it originally contained 36 cm3? ​

Find the future value of an ordinary annuity of $67 paid quarterly for 4 years, if the interest rate is 6%, compounded quarterly. Round your answer to the nearest cent. ​

What does 040 represent in the following equation? ​ ​

Which of the following expresses the sum of the first 27 terms of the geometric sequence 9, -6, 4....? ​

A sinking fund is established to discharge a debt of $70,000 in 8 years. If deposits are made at the end of each 6-month period and interest is paid at the annual rate of 6%, compounded semiannually, what is the amount of each deposit? Round your answer to the nearest cent. ​

If a population of 6 million begins to increase at a rate of 0.2% each month, in how many months will it be 9 million? Round your answer to two decimal places. ​

If $6,000 is deposited at the end of each half year in an account that earns an annual rate of 6.3% compounded semiannually, how long will it be before the account contains $170,000? Round your answer to two decimal places. ​

If inflation causes the cost of automobiles to increase by 3.5% each year, what should a car cost today if it cost $21,000 4 years ago? Round your answer to the nearest cent.

Suppose a new business makes a $2,000 profit in its first month and has its profit increase by 14% each month for the next 2 years. How much profit will the business earn in its 13^th month? Round your answer to the nearest cent.

Find the next three terms of the geometric sequence. 25, 5, 1,...

Suppose a new business makes a $1,000 profit in its first month and has its profit increase by 9% each month for the next 2 years. How much profit will it earn in its first year? Round your answer to the nearest cent.

How long does it take for an account containing $5,500 to be worth $13,600 if the money is invested at 12% compounded monthly? Round your answer to the one decimal place.

Write an expression that gives the requested term or sum. The sum of the first 12 terms of the geometric sequence with first term 6 and common ratio 7.

What is the 7th term of the geometric sequence with first term 5 and common ratio 2?

Find the next three terms of the geometric sequence. 3, 9, 27,...

Find the future value of an annuity due of $1,700 each month for 4 years if the annual interest rate is 11%, compounded monthly. Round your answer to the nearest cent.

Find S : . Round your answer to the nearest dollar.

A pump removes of the water in a container with every stroke. How much water remains in the container after 3 strokes if it originally contained 36 cm³?

Find the future value of an ordinary annuity of $67 paid quarterly for 4 years, if the interest rate is 6%, compounded quarterly. Round your answer to the nearest cent.

What does 040 represent in the following equation?

Which of the following expresses the sum of the first 27 terms of the geometric sequence 9, -6, 4....?

A sinking fund is established to discharge a debt of $70,000 in 8 years. If deposits are made at the end of each 6-month period and interest is paid at the annual rate of 6%, compounded semiannually, what is the amount of each deposit? Round your answer to the nearest cent.

If a population of 6 million begins to increase at a rate of 0.2% each month, in how many months will it be 9 million? Round your answer to two decimal places.

If $6,000 is deposited at the end of each half year in an account that earns an annual rate of 6.3% compounded semiannually, how long will it be before the account contains $170,000? Round your answer to two decimal places.