Question 1

Find the effective rate corresponding to the given nominal rate 10% compounded semi-annually. Please express your answer as a fraction.

Accepted Answer

The answer of Find the effective rate corresponding to the...

Question 2

Find the effective rate of interest corresponding to a nominal rate of 5%/year compounded annually, semiannually, quarterly, and monthly. Round the answers to two decimal places, if necessary.

Accepted Answer

The answer of Find the effective rate of interest corresponding...

Question 3

Georgia purchased a house in 1997 for $220,000. In 2003 she sold the house and made a net profit of $41,000. Find the effective annual rate of return on her investment over the 6-yr period. Please round the answer to the nearest tenth of percent.
__________%/yr

Accepted Answer

The answer of Georgia purchased a house in 1997 for...

Question 4

A young man is the beneficiary of a trust fund established for him 21 years ago at his birth. If the original amount placed in trust was $5,000, how much will he receive if the money has earned interest at the rate of 6%/year compounded annually? Compounded quarterly? Compounded monthly? Please round your answers to the nearest dollar.
$__________ annually
$__________ quarterly
$__________ monthly

Accepted Answer

The answer of A young man is the beneficiary of...

Question 5

Today a typical family of four spends $600/month for food. If inflation occurs at the rate of 4%/year over the next 8 yr, how much should the typical family of four expect to spend for food 8 yr from now? Please round the answer to the nearest cent.
$ __________

Accepted Answer

The answer of Today a typical family of four spends...

Question 6

In the last 3 years, mutual fund A grew at the rate of 10.5%/year compounded quarterly. Over the same period, mutual fund B grew at the rate of 10.6%/year compounded semi-annually. Which mutual fund has a better rate of return? (Answer A or B.)

Accepted Answer

The answer of In the last 3 years, mutual fund...

Question 7

Find the amount of an ordinary annuity of 5 yearly payments of $600 that earn interest at 5% per year, compounded annually. ​

Accepted Answer

To find the amount of an ordinary annuity, we can use the formula:

A = P * [(1 + r)^n - 1] / r

where:
A = amount of annuity
P = periodic payment
r = interest rate per period
n = number of periods

In this case, P = $600, r = 0.05 (5% per year), n = 5, and the annuity is compounded annually. Substituting these values into the formula, we get:

A = $600 * [(1 + 0.05)^5 - 1] / 0.05
A = $600 * (1.27628) / 0.05
A = $15,315.38

However, this is the total amount paid over 5 years. To find the amount of each payment, we divide by the number of periods:

Amount of each payment = A / n
Amount of each payment = $15,315.38 / 5
Amount of each payment = $3,063.08

Therefore, the best choice is B: $3,315.38 (rounded to the nearest cent), which is the total amount paid over 5 years divided by the number of periods.

Question 8

Find how much money should be deposited in a bank paying interest at the rate of 10.5%/year compounded quarterly so that at the end of 5 years the accumulated amount will be $60,000. Round your answer to the nearest cent.
$ __________

Accepted Answer

The answer of Find how much money should be deposited...

Question 9

Carlos invested $4,000 in a money market mutual fund that pays interest on a daily basis. The balance in his account at the end of 8 mo (245 days) was $4,163. Find the effective rate at which Carlos's account earned interest over this period (assume a 365-day year). Round your answer to the nearest hundredth of a percent. r_eff = __________ %/year

Accepted Answer

The answer of Carlos invested $4,000 in a money market...

Question 10

Find the interest rate needed for an investment of $3,000 to grow to an amount of $4,000 in 3 yr if interest is compounded continuously. Please round the answer to the nearest hundredth of percent.
__________ %/yr

Accepted Answer

The answer of Find the interest rate needed for an...

Question 11

In order to help finance the purchase of a new house, the Abdullahs have decided to apply for a short-term loan (a bridge loan) in the amount of $180,000 for a term of 2 mo. If the bank charges simple interest at the rate of 13%/year, how much will the Abdullahs owe the bank at the end of the term?
$ __________

Accepted Answer

The answer of In order to help finance the purchase...

Question 12

Find the simple interest on a $500 investment made for 5 years at an interest rate of 9%/year. What is the accumulated amount?

Accepted Answer

The answer of Find the simple interest on a $500...

Question 13

The Kwans are planning to buy a house 4 years from now. Housing experts in their area have estimated that the cost of a home will increase at a rate of 6%/year during that period. If this economic prediction holds true, how much can the Kwans expect to pay for a house that currently costs $130,000? Please round your answer to the nearest dollar.
$ __________

Accepted Answer

The answer of The Kwans are planning to buy a...

Question 14

Investment A offers a 9% return compounded semiannually, and investment B offers a 8.87% return compounded continuously. Which investment has a higher rate of return over a 4-yr period? (Enter A or B.)

Accepted Answer

The answer of Investment A offers a 9% return compounded...

Question 15

Anthony invested a sum of money 4 yr ago in a savings account that has since paid interest at the rate of 9%/year compounded quarterly. His investment is now worth $22,841.96. How much did he originally invest? Please round the answer to the nearest cent.
$ __________

Accepted Answer

The answer of Anthony invested a sum of money 4...

Question 16

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
​
Susan's salary increased from $55,000/year to $65,000/year over a 6-year period. Therefore, Susan got annual increases of 6% over that period.

Accepted Answer

If Susan had gotten annual increases of 6 percent over 6 years, her salary would have been 11eab448_e809_2657_acdb_f92d15a210a3_TB6027_11 , or approximately $78,018.55 after 6 years, not $65,000.

Question 17

The future value of an annuity can be found by adding together all the payments that are paid into the account and all the interests they have earned. ​

Accepted Answer

The statement is true. The future value of an annuity is the sum of all the payments made into the account, plus any interest earned on those payments.

Question 18

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
​
If compound interest is converted annually, then the accumulated amount after t years is not the same as the accumulated amount under simple interest over t yr.

Accepted Answer

Under compound interest A = P(1 + r)^t (m = 1), and under simple interest A = P(1 + rt). For example, if r = 7% , P = $1,000 , t = 3yr , so under compound interest A = 1,225 , and under simple interest A = 1,210.

Question 19

From age 25 to age 40, Jessica deposited $150 at the end of each month into a tax-free retirement account. She made no withdrawals or further contributions until age 65. Alex made deposits of $300 into his tax-free retirement account from age 40 to age 65. If both accounts earned interest at the rate of 5%/year compounded monthly, who ends up with a bigger nest egg upon reaching the age of 65, Jessica or Alex? ​

Accepted Answer

Jessica's contributions benefit from a longer period of compound interest, allowing her account to grow more despite her lower monthly contribution compared to Alex.

Question 20

Five and a half years ago, Chris invested $9,000 in a retirement fund that grew at the rate of 10.44%/year compounded quarterly. What is his account worth today? Please round the answer to the nearest cent.
$ __________

Accepted Answer

The answer of Five and a half years ago, Chris...

Quiz 5: Mathematics of Finance

Find the effective rate corresponding to the given nominal rate 10% compounded semi-annually. Please express your answer as a fraction.

Find the effective rate of interest corresponding to a nominal rate of 5%/year compounded annually, semiannually, quarterly, and monthly. Round the answers to two decimal places, if necessary.

Georgia purchased a house in 1997 for $220,000. In 2003 she sold the house and made a net profit of $41,000. Find the effective annual rate of return on her investment over the 6-yr period. Please round the answer to the nearest tenth of percent. __________%/yr

Today a typical family of four spends $600/month for food. If inflation occurs at the rate of 4%/year over the next 8 yr, how much should the typical family of four expect to spend for food 8 yr from now? Please round the answer to the nearest cent. $ __________

In the last 3 years, mutual fund A grew at the rate of 10.5%/year compounded quarterly. Over the same period, mutual fund B grew at the rate of 10.6%/year compounded semi-annually. Which mutual fund has a better rate of return? (Answer A or B.)

Find the amount of an ordinary annuity of 5 yearly payments of $600 that earn interest at 5% per year, compounded annually.

Find how much money should be deposited in a bank paying interest at the rate of 10.5%/year compounded quarterly so that at the end of 5 years the accumulated amount will be $60,000. Round your answer to the nearest cent. $ __________

Find the interest rate needed for an investment of $3,000 to grow to an amount of $4,000 in 3 yr if interest is compounded continuously. Please round the answer to the nearest hundredth of percent. __________ %/yr

Find the simple interest on a $500 investment made for 5 years at an interest rate of 9%/year. What is the accumulated amount?

Investment A offers a 9% return compounded semiannually, and investment B offers a 8.87% return compounded continuously. Which investment has a higher rate of return over a 4-yr period? (Enter A or B.)

Anthony invested a sum of money 4 yr ago in a savings account that has since paid interest at the rate of 9%/year compounded quarterly. His investment is now worth $22,841.96. How much did he originally invest? Please round the answer to the nearest cent. $ __________

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. Susan's salary increased from $55,000/year to $65,000/year over a 6-year period. Therefore, Susan got annual increases of 6% over that period.

The future value of an annuity can be found by adding together all the payments that are paid into the account and all the interests they have earned.

Five and a half years ago, Chris invested $9,000 in a retirement fund that grew at the rate of 10.44%/year compounded quarterly. What is his account worth today? Please round the answer to the nearest cent. $ __________

Quiz 5: Mathematics of Finance

Find the effective rate corresponding to the given nominal rate 10% compounded semi-annually. Please express your answer as a fraction.

Find the effective rate of interest corresponding to a nominal rate of 5%/year compounded annually, semiannually, quarterly, and monthly. Round the answers to two decimal places, if necessary.

Georgia purchased a house in 1997 for $220,000. In 2003 she sold the house and made a net profit of $41,000. Find the effective annual rate of return on her investment over the 6-yr period. Please round the answer to the nearest tenth of percent. __________%/yr

Today a typical family of four spends $600/month for food. If inflation occurs at the rate of 4%/year over the next 8 yr, how much should the typical family of four expect to spend for food 8 yr from now? Please round the answer to the nearest cent. $ __________

In the last 3 years, mutual fund A grew at the rate of 10.5%/year compounded quarterly. Over the same period, mutual fund B grew at the rate of 10.6%/year compounded semi-annually. Which mutual fund has a better rate of return? (Answer A or B.)

Find the amount of an ordinary annuity of 5 yearly payments of $600 that earn interest at 5% per year, compounded annually. ​

Find how much money should be deposited in a bank paying interest at the rate of 10.5%/year compounded quarterly so that at the end of 5 years the accumulated amount will be $60,000. Round your answer to the nearest cent. $ __________

Find the interest rate needed for an investment of $3,000 to grow to an amount of $4,000 in 3 yr if interest is compounded continuously. Please round the answer to the nearest hundredth of percent. __________ %/yr

Find the simple interest on a $500 investment made for 5 years at an interest rate of 9%/year. What is the accumulated amount?

Investment A offers a 9% return compounded semiannually, and investment B offers a 8.87% return compounded continuously. Which investment has a higher rate of return over a 4-yr period? (Enter A or B.)

Anthony invested a sum of money 4 yr ago in a savings account that has since paid interest at the rate of 9%/year compounded quarterly. His investment is now worth $22,841.96. How much did he originally invest? Please round the answer to the nearest cent. $ __________

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. ​ Susan's salary increased from $55,000/year to $65,000/year over a 6-year period. Therefore, Susan got annual increases of 6% over that period.

The future value of an annuity can be found by adding together all the payments that are paid into the account and all the interests they have earned. ​

Five and a half years ago, Chris invested $9,000 in a retirement fund that grew at the rate of 10.44%/year compounded quarterly. What is his account worth today? Please round the answer to the nearest cent. $ __________

Find the amount of an ordinary annuity of 5 yearly payments of $600 that earn interest at 5% per year, compounded annually.

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. Susan's salary increased from $55,000/year to $65,000/year over a 6-year period. Therefore, Susan got annual increases of 6% over that period.

The future value of an annuity can be found by adding together all the payments that are paid into the account and all the interests they have earned.