Question 1

What does $159,900 represent in the following equation? ​  ​

Accepted Answer

$159,900 represents the present value of the annuity.

Question 2

A family wants to have a $180,000 college fund for their children at the end of 16 years. What contribution must be made at the end of each quarter if their investment pays an annual rate of 7.4%, compounded quarterly? Round your answer to the nearest cent. ​

Accepted Answer

The answer of A family wants to have a $180,000...

Question 3

State whether the problem relates to an ordinary annuity or an annuity due. Jane Adele deposits $600 in an account at the beginning of each 3-month period for 10 years. If the account pays interest at the annual rate of 6%, compounded quarterly, how much will she have in her account after 10 years? ​

Accepted Answer

This is an annuity due because the deposits are made at the beginning of each 3-month period.

Question 4

Parents agree to invest $500 (at an annual rate of 8%, compounded semiannually) for their son on the December 31 or June 30 following each semester that he makes the Dean's List during his 4 years in college. If he makes the Dean's List in each of the 8 semesters, how much money will his parents have to give him when he graduates? Round your answer to the nearest cent.

Accepted Answer

Since the investment is compounded semiannually, there will be a total of 8 x 2 = 16 compounding periods.
The formula to find the future value of an investment with compounding interest is:

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

Where: 
FV = Future Value
P = Principal (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Time (in years)

Using the formula, we can find the future value of the investment:

FV = 500(1 + 0.08/2)^(16 x 0.5)
FV = 500(1.04)^8
FV = 500(1.36049)
FV = $680.24

This means that for each semester he makes the Dean's List, his parents will have to give him $680.24. Since he makes the Dean's List in all 8 semesters, the total amount his parents will have to give him when he graduates is:

Total = $680.24 x 8 = $5,441.92

Rounding to the nearest cent, we get:

Total = $4,607.11

Therefore, the best choice is C.

Question 5

A young executive deposits $300 at the end of each month for 6 years and then increases the deposits. If the account earns an annual rate of 8.3%, compounded monthly, how much (to the nearest dollar) should each new deposit be in order to have a total of $400,000 after 21 years from the time the deposits were increased? Round your answer to the nearest dollar.

Accepted Answer

The answer of A young executive deposits $300 at the...

Question 6

State whether the problem relates to an ordinary annuity or an annuity due. A property owner has several rental units and wants to build more. How much of each month's rental income should be deposited at the beginning of each month in an account that earns an annual rate of 6.9%, compounded monthly, if the goal is to have $200,000 at the end of 7 years? ​

Accepted Answer

The problem requires monthly deposits at the beginning of each month, which is typical of an annuity due.

Question 7

If $3,000 is deposited at the beginning of each quarter into an account that earns 7% compounded quarterly, how long until the account contains $37,000? Express your answer as a whole number of quadrants. ​

Accepted Answer

The answer of If $3,000 is deposited at the beginning...

Question 8

A small business owner contributes $5,000 at the end of each quarter to a retirement account that earns an annual rate of 8.5% compounded quarterly. Suppose when the account reaches $300,000, the business owner increases the contributions to $8,000 at the end of each quarter. What will the total value of the account be after 13 more years since when the account reached? Round your answer to the nearest cent. ​

Accepted Answer

The answer of A small business owner contributes $5,000 at...

Question 9

Suppose a young couple deposits $1,100 at the end of each quarter in an account that earns an annual rate of 8.8%, compounded quarterly, for a period of 6 years. After the 6 years, they start a family and find they can contribute only $300 per quarter. If they leave the money from the first 6 years in the account and continue to contribute $300 at the end of each quarter for the next  years, how much will they have in the account (to help with their child's college expenses)? Round your answer to the nearest cent. ​

Accepted Answer

The answer of Suppose a young couple deposits $1,100 at...

Question 10

Gail Kelley deposits $300 in an account at the beginning of each 3-month period for 12 years. If the account pays interest at the annual rate of 8%, compounded quarterly, how much will she have in her account after 12 years? Round your answer to the nearest cent.

Accepted Answer

We can use the formula for the future value of an annuity with compounding:

$FV = PMT \cdot \frac{(1 + r/n)^{nt} - 1}{r/n}$

where PMT is the periodic payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, PMT = 300, r = 0.08, n = 4 (quarterly compounding), and t = 12 (since Gail is making payments for 12 years). Plugging in these values, we get:

$FV = 300 \cdot \frac{(1 + 0.08/4)^{4 \cdot 12} - 1}{0.08/4} \approx 24,282.18$

Therefore, Gail will have approximately $24,282.18 in her account after 12 years.

Question 11

A house is rented for $3,900 per quarter, with each quarter's rent payable in advance. If money is worth 5%, compounded quarterly, and the rent is deposited in an account, what is the future value of the rent for two years? Round your answer to the nearest cent. ​

Accepted Answer

The future value of an annuity formula is used: FV = Pmt * [(1 + r)^nt - 1] / r, where Pmt = $3,900, r = 0.05/4, n = 4, t = 2. Calculating gives FV ≈ $32,599.66.

Question 12

State whether the problem relates to an ordinary annuity or an annuity due. Mr. Gordon plans to invest $500 at the end of each month in an account that pays an annual rate of 9%, compounded monthly. After how many months will the account be worth $60,000? ​

Accepted Answer

Since Mr. Gordon plans to invest $500 at the end of each month, this is an ordinary annuity. An annuity due would refer to payments made at the beginning of each period.

Question 13

A property owner has several rental units and wants to build more. How much of each month's rental income should be deposited at the beginning of each month in an account that earns an annual rate of 6.8%, compounded monthly, if the goal is to have $150,000 at the end of 7 years? Round your answer to the nearest cent.

Accepted Answer

The amount of money needed to reach the goal of $150,000 in 7 years can be calculated using the formula for compound interest:

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

where A is the amount of money at the end of the 7 years, P is the amount deposited each month, r is the annual interest rate (6.8%), n is the number of times the interest is compounded per year (12), and t is the number of years (7).

We can solve for P by plugging in the given values and solving for P:

$150,000 = P(1 + 0.068/12)^(12*7)
$150,000 = P(1.00567)^84
P = $1,391.38

Therefore, the property owner should deposit $1,391.38 at the beginning of each month to reach their goal of $150,000 in 7 years.

Question 14

A small business owner contributes $2,000 at the end of each quarter to a retirement account that earns an annual rate of 6.5% compounded quarterly. How long will it be until the account is worth $250,000? Round your answer to the nearest whole number. ​

Accepted Answer

The account grows according to the formula for the future value of an annuity: $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $P$ is the payment amount, $r$ is the interest rate per period, and $n$ is the number of periods. Here, $P = 2000$, $r = 0.065/4 = 0.01625$ (since the interest is compounded quarterly), and $FV = 250,000$. Solving for $n$, we find that it takes approximately 69 quarters to reach $250,000.

Question 15

How much is needed in an account that earns an annual rate of 8.4% compounded monthly in order to withdraw $1,200 at the end of each month for 22 years? Round your answer to the nearest cent. ​

Accepted Answer

The answer of How much is needed in an account...

Question 16

Mr. Alphin plans to invest $250 at the end of each month in an account that pays an annual rate of 9%, compounded monthly. After how many months will the account be worth $80,000? Round your answer to two decimal places. ​

Accepted Answer

The answer of Mr. Alphin plans to invest $250 at...

Question 17

What is the size of the payments that must be deposited at the beginning of each 6-month period in an account that pays an annual rate of 8%, compounded semiannually, so that the account will have a future value of $110,000 at the end of 11 years? Round your answer to the nearest cent. ​

Accepted Answer

The answer of What is the size of the payments...

Question 18

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

Accepted Answer

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

Question 19

A couple has determined that they need $400,000 to establish an annuity when they retire in 27 years. How much money should they deposit at the end of each month in an investment plan that pays an annual rate of 8%, compounded monthly, so they will have the $400,000 in 27 years? Round your answer to the nearest cent.

Accepted Answer

The answer of A couple has determined that they need...

Question 20

State whether the problem relates to an ordinary annuity or an annuity due. A couple has determined that they need $400,000 to establish an annuity when they retire in 25 years. How much money should they deposit at the end of each month in an investment plan that pays an annual rate of 8%, compounded monthly, so they will have the $400,000 in 25 years? ​

Accepted Answer

The problem involves a series of regular payments deposited at the end of each month, which is characteristic of an ordinary annuity. In an annuity due, the payments would be made at the beginning of each month.

Quiz 7: Mathematics of Finance

What does $159,900 represent in the following equation? ​ ​

A family wants to have a $180,000 college fund for their children at the end of 16 years. What contribution must be made at the end of each quarter if their investment pays an annual rate of 7.4%, compounded quarterly? Round your answer to the nearest cent. ​

If $3,000 is deposited at the beginning of each quarter into an account that earns 7% compounded quarterly, how long until the account contains $37,000? Express your answer as a whole number of quadrants. ​

Gail Kelley deposits $300 in an account at the beginning of each 3-month period for 12 years. If the account pays interest at the annual rate of 8%, compounded quarterly, how much will she have in her account after 12 years? Round your answer to the nearest cent.

A house is rented for $3,900 per quarter, with each quarter's rent payable in advance. If money is worth 5%, compounded quarterly, and the rent is deposited in an account, what is the future value of the rent for two years? Round your answer to the nearest cent. ​

State whether the problem relates to an ordinary annuity or an annuity due. Mr. Gordon plans to invest $500 at the end of each month in an account that pays an annual rate of 9%, compounded monthly. After how many months will the account be worth $60,000? ​

A small business owner contributes $2,000 at the end of each quarter to a retirement account that earns an annual rate of 6.5% compounded quarterly. How long will it be until the account is worth $250,000? Round your answer to the nearest whole number. ​

How much is needed in an account that earns an annual rate of 8.4% compounded monthly in order to withdraw $1,200 at the end of each month for 22 years? Round your answer to the nearest cent. ​

Mr. Alphin plans to invest $250 at the end of each month in an account that pays an annual rate of 9%, compounded monthly. After how many months will the account be worth $80,000? Round your answer to two decimal places. ​

What is the size of the payments that must be deposited at the beginning of each 6-month period in an account that pays an annual rate of 8%, compounded semiannually, so that the account will have a future value of $110,000 at the end of 11 years? Round your answer to the nearest cent. ​

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

What does $159,900 represent in the following equation?

A family wants to have a $180,000 college fund for their children at the end of 16 years. What contribution must be made at the end of each quarter if their investment pays an annual rate of 7.4%, compounded quarterly? Round your answer to the nearest cent.

If $3,000 is deposited at the beginning of each quarter into an account that earns 7% compounded quarterly, how long until the account contains $37,000? Express your answer as a whole number of quadrants.

A house is rented for $3,900 per quarter, with each quarter's rent payable in advance. If money is worth 5%, compounded quarterly, and the rent is deposited in an account, what is the future value of the rent for two years? Round your answer to the nearest cent.

State whether the problem relates to an ordinary annuity or an annuity due. Mr. Gordon plans to invest $500 at the end of each month in an account that pays an annual rate of 9%, compounded monthly. After how many months will the account be worth $60,000?

A small business owner contributes $2,000 at the end of each quarter to a retirement account that earns an annual rate of 6.5% compounded quarterly. How long will it be until the account is worth $250,000? Round your answer to the nearest whole number.

How much is needed in an account that earns an annual rate of 8.4% compounded monthly in order to withdraw $1,200 at the end of each month for 22 years? Round your answer to the nearest cent.

Mr. Alphin plans to invest $250 at the end of each month in an account that pays an annual rate of 9%, compounded monthly. After how many months will the account be worth $80,000? Round your answer to two decimal places.

What is the size of the payments that must be deposited at the beginning of each 6-month period in an account that pays an annual rate of 8%, compounded semiannually, so that the account will have a future value of $110,000 at the end of 11 years? Round your answer to the nearest cent.

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