Question 1

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 correct answer is A because the total amount after 11 years is $4,010.84. The amount after 3 years in the first account is $1,400 + (1,400 * 0.10 * 3) = $1,820. The amount after 8 years in the second account is $1,820 * (1 + 0.10/4)^(4*8) = $4,010.84.

Question 2

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

The future value of an annuity due can be calculated using the formula FV = P * [(1 + r)^nt - 1] * (1 + r) / r, where P is the payment amount, r is the monthly interest rate, n is the number of compounding periods per year, and t is the number of years. Here, P = $1,700, r = 0.11/12, n = 12, and t = 4. Plugging these values into the formula gives the future value closest to $102,859.77.

Question 3

A sinking fund is established to discharge a debt of $80,000 in 11 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 4

Find the next three terms of the geometric sequence. ​
4, 16, 64,...
​

Accepted Answer

Each term in the sequence is obtained by multiplying the previous term by 4 (since 16/4 = 4 and 64/16 = 4). Therefore, the next three terms after 64 are 64*4 = 256, 256*4 = 1024, and 1024*4 = 4096.

Question 5

What is the 9th term of the geometric sequence with first term 5 and common ratio 2? ​

Accepted Answer

The nth term of a geometric sequence with first term $a$ and common ratio $r$ is $a\cdot r^{n-1}$. Therefore, the ninth term of the given sequence is $5\cdot2^{8}=1,280$. Thus, the answer is $\boxed{	extbf{(E)}}$.

Question 6

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 7

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 correct answer is found by first calculating the future value of the annuity (the $2,000 annual deposit for 5 years) using the future value of an annuity formula, and then calculating the future value of this amount over the next 25 years using the future value of a single sum formula. Both calculations use the 8.1% annual interest rate.

Question 8

How long does it take for an account containing $7,000 to be worth $15,900 if the money is invested at 9% compounded monthly? Round your answer to the one decimal place. ​

Accepted Answer

To find the time it takes for the investment to grow, we use the formula for compound interest: A = P(1 + r/n)^(nt). Here, A = $15,900, P = $7,000, r = 0.09, n = 12. Solving for t gives approximately 9.1 years.

Question 9

Find the future value of an ordinary annuity of $66 paid quarterly for 6 years, if the interest rate is 8%, compounded quarterly. Round your answer to the nearest cent. ​

Accepted Answer

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

Question 10

Find the next three terms of the geometric sequence. ​
256, 16, 1,...
​

Accepted Answer

The sequence is a geometric sequence where each term is divided by 16 to get the next term (256/16 = 16, 16/16 = 1). Continuing this pattern, the next three terms are 1/16 = 0.0625, 0.0625/16 = 0.00390625, and 0.00390625/16 = 0.0002441406.

Question 11

What does 040 represent in the following equation? ​  ​

Accepted Answer

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

Question 12

If a population of 9 million begins to increase at a rate of 0.33% each month, in how many months will it be 14 million? Round your answer to two decimal places. ​

Accepted Answer

We can use the formula for exponential growth: A = P(1+r)^t, where A is the final amount, P is the initial amount, r is the growth rate as a decimal, and t is the time in months.

Plugging in the given values, we get:

14,000,000 = 9,000,000(1+0.0033)^t

Divide both sides by 9,000,000:

1.55556... = (1+0.0033)^t

Take the natural log of both sides:

ln(1.55556...) = ln(1+0.0033)t

Divide both sides by ln(1+0.0033):

t = ln(1.55556...)/ln(1+0.0033)

Using a calculator, we get t ≈ 134.11 months.

Therefore, the answer is C: 134.11 months.

Question 13

Which of the following expresses the sum of the first 29 terms of the geometric sequence  ....? ​

Accepted Answer

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

Question 14

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

The answer of If inflation causes the cost of automobiles...

Question 15

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

To calculate the profit earned in the first year, we need to first calculate the profit earned in the first 12 months.

Profit earned in the first month = $1,000

Profit earned in the second month = $1,000 + 9% of $1,000 = $1,090

Profit earned in the third month = $1,090 + 9% of $1,090 = $1,188.10

Continuing this pattern for 12 months, we get:

Profit earned in the first year = $1,000 + $1,090 + $1,188.10 + ... + (9% of profit earned in the 11th month) 
= $20,140.72

Therefore, the best choice is D.

Question 16

Suppose a new business makes a $1,000 profit in its first month and has its profit increase by 13% each month for the next 2 years. How much profit will the business earn in its 15^th month? Round your answer to the nearest cent.

Accepted Answer

The answer of Suppose a new business makes a $1,000...

Question 17

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

After one stroke, the container will have 36 - 11eb0d3b_981d_98f6_9790_a958dc994899_TB1243_11 = 25 cm³ of water remaining. After two strokes, the container will have 25 - 11eb0d3b_981d_98f6_9790_a958dc994899_TB1243_11 = 14 cm³ of water remaining. After three strokes, the container will have 14 - 11eb0d3b_981d_98f6_9790_a958dc994899_TB1243_11 = 3 cm³ of water remaining. Therefore, the answer is A) 3 cm³.

Question 18

If $5,000 is deposited at the end of each half year in an account that earns an annual rate of 6.0% compounded semiannually, how long will it be before the account contains $145,000? Round your answer to two decimal places. ​

Accepted Answer

The answer of If $5,000 is deposited at the end...

Question 19

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

Accepted Answer

Without knowing the specific context of the code, it is impossible to determine the true value of S. However, rounding the answer to the nearest dollar and based on the given options, D is the closest to the calculated result of $234,346.85. Therefore, D would be the best choice.

Question 20

Suppose that Bob delays starting an IRA for the first 10 years he works but then makes $2,500 deposits at the end of each of the next 15 years. If the annual interest rate is 7.2%, 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

To start, we need to calculate how much the $2,500 deposits at the end of each of the next 15 years will grow to in 30 years. We can use the formula for future value of an annuity to find this amount:

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

where PMT is the deposit amount, r is the interest rate, and n is the number of periods. Plugging in the values from the problem, we get:

FV = $2,500 x (((1 + 0.072)^15 - 1) / 0.072) = $73,316.66

Next, we need to calculate how much Bob will have after leaving the money in the account for 5 additional years. To do this, we can use the formula for future value of a lump sum:

FV = PV x (1 + r)^n

where PV is the present value (which in this case is the amount we just calculated, $73,316.66), r is the interest rate, and n is the number of periods. Plugging in the values from the problem, we get:

FV = $73,316.66 x (1 + 0.072)^5 = $90,320.64

Therefore, the answer is A, $90,320.64.

Quiz 7: Mathematics of Finance

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.

A sinking fund is established to discharge a debt of $80,000 in 11 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.

Find the next three terms of the geometric sequence. 4, 16, 64,...

What is the 9th term of the geometric sequence with first term 5 and common ratio 2?

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.

How long does it take for an account containing $7,000 to be worth $15,900 if the money is invested at 9% compounded monthly? Round your answer to the one decimal place.

Find the future value of an ordinary annuity of $66 paid quarterly for 6 years, if the interest rate is 8%, compounded quarterly. Round your answer to the nearest cent.

Find the next three terms of the geometric sequence. 256, 16, 1,...

What does 040 represent in the following equation?

If a population of 9 million begins to increase at a rate of 0.33% each month, in how many months will it be 14 million? Round your answer to two decimal places.

Which of the following expresses the sum of the first 29 terms of the geometric sequence ....?

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 $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.

Suppose a new business makes a $1,000 profit in its first month and has its profit increase by 13% each month for the next 2 years. How much profit will the business earn in its 15^th month? Round your answer to the nearest cent.

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?

If $5,000 is deposited at the end of each half year in an account that earns an annual rate of 6.0% compounded semiannually, how long will it be before the account contains $145,000? Round your answer to two decimal places.

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

Quiz 7: Mathematics of Finance

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. ​

A sinking fund is established to discharge a debt of $80,000 in 11 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. ​

Find the next three terms of the geometric sequence. ​ 4, 16, 64,... ​

What is the 9th term of the geometric sequence with first term 5 and common ratio 2? ​

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. ​

How long does it take for an account containing $7,000 to be worth $15,900 if the money is invested at 9% compounded monthly? Round your answer to the one decimal place. ​

Find the future value of an ordinary annuity of $66 paid quarterly for 6 years, if the interest rate is 8%, compounded quarterly. Round your answer to the nearest cent. ​

Find the next three terms of the geometric sequence. ​ 256, 16, 1,... ​

What does 040 represent in the following equation? ​ ​

If a population of 9 million begins to increase at a rate of 0.33% each month, in how many months will it be 14 million? Round your answer to two decimal places. ​

Which of the following expresses the sum of the first 29 terms of the geometric sequence ....? ​

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 $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. ​

Suppose a new business makes a $1,000 profit in its first month and has its profit increase by 13% each month for the next 2 years. How much profit will the business earn in its 15th month? Round your answer to the nearest cent. ​

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? ​

If $5,000 is deposited at the end of each half year in an account that earns an annual rate of 6.0% compounded semiannually, how long will it be before the account contains $145,000? Round your answer to two decimal places. ​

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

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.

A sinking fund is established to discharge a debt of $80,000 in 11 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.

Find the next three terms of the geometric sequence. 4, 16, 64,...

What is the 9th term of the geometric sequence with first term 5 and common ratio 2?

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.

How long does it take for an account containing $7,000 to be worth $15,900 if the money is invested at 9% compounded monthly? Round your answer to the one decimal place.

Find the future value of an ordinary annuity of $66 paid quarterly for 6 years, if the interest rate is 8%, compounded quarterly. Round your answer to the nearest cent.

Find the next three terms of the geometric sequence. 256, 16, 1,...

What does 040 represent in the following equation?

If a population of 9 million begins to increase at a rate of 0.33% each month, in how many months will it be 14 million? Round your answer to two decimal places.

Which of the following expresses the sum of the first 29 terms of the geometric sequence ....?

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 $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.

Suppose a new business makes a $1,000 profit in its first month and has its profit increase by 13% each month for the next 2 years. How much profit will the business earn in its 15^th month? Round your answer to the nearest cent.

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?

If $5,000 is deposited at the end of each half year in an account that earns an annual rate of 6.0% compounded semiannually, how long will it be before the account contains $145,000? Round your answer to two decimal places.

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