Question 1

What annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $2,600?

Accepted Answer

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Question 2

What's the future value of $4,500 after 5 years if the appropriate interest rate is 6%,compounded semiannually?

Accepted Answer

To calculate future value, we can use the formula FV = PV*(1+r/n)^(n*t), where PV is the present value, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

Plugging in the given values, we get FV = 4500*(1+0.06/2)^(2*5) = $6,047.62. Therefore, the best choice is B.

Question 3

Your father paid $10,000 (CF at t = 0)for an investment that promises to pay $750 at the end of each of the next 5 years,then an additional lump sum payment of $11,500 at the end of the 5th year.What is the expected rate of return on this investment?

Accepted Answer

The expected rate of return is the internal rate of return (IRR) that equates the present value of cash inflows to the initial investment. Solving for IRR using the given cash flows results in approximately 9.96%.

Question 4

What's the future value of $1,600 after 5 years if the appropriate interest rate is 6%,compounded monthly?

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Question 5

What is the present value of the following cash flow stream at a rate of 13.5%? ​

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Question 6

Suppose your credit card issuer states that it charges a 23.75% nominal annual rate,but you must make monthly payments,which amounts to monthly compounding.What is the effective annual rate?

Accepted Answer

To find the effective annual rate, we need to take into account the effect of compounding. Using the formula for effective annual rate (EAR), we get:

EAR = (1 + r/n)^n - 1

where r is the nominal annual rate (23.75%) and n is the number of compounding periods per year. Since we have monthly compounding, n = 12. Plugging in the values, we get:

EAR = (1 + 0.2375/12)^12 - 1 = 0.2651 or 26.51%

Therefore, the best choice is C.

Question 7

Master Card and other credit card issuers must by law print the Annual Percentage Rate (APR)on their monthly statements.If the APR is stated to be 19.25%,with interest paid monthly,what is the card's EFF%?

Accepted Answer

To calculate the EFF% (Effective Annual Interest Rate), we can use the following formula: EFF% = (1 + i/m)^m - 1, where i is the stated APR and m is the number of times interest is compounded per year. In this case, interest is paid monthly, so m = 12. Plugging in the values, we get: EFF% = (1 + 0.1925/12)^12 - 1 = 0.2104 or 21.04%. Therefore, the correct answer is A.

Question 8

At a rate of 5.0%,what is the future value of the following cash flow stream? ​

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Question 9

Suppose Community Bank offers to lend you $10,000 for one year at a nominal annual rate of 19.50%,but you must make interest payments at the end of each quarter and then pay off the $10,000 principal amount at the end of the year.What is the effective annual rate on the loan?

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Question 10

Your girlfriend just won the Florida lottery.She has the choice of $10,800,000 today or a 20-year annuity of $1,050,000,with the first payment coming one year from today.What rate of return is built into the annuity? Disregard taxes.

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Question 11

What's the present value of $17,500 discounted back 5 years if the appropriate interest rate is 4.5%,compounded semiannually?

Accepted Answer

Using the formula for present value, we have:

PV = FV / (1 + (r/n))^(n*t)

where PV is the present value, FV is the future value, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

Substituting the given values, we get:

PV = 17,500 / (1 + (0.045/2))^(2*5)
PV = 17,500 / (1.0225)^10
PV = 17,500 / 1.248035
PV = 14,008.93

Therefore, the present value of $17,500 discounted back 5 years at an interest rate of 4.5%, compounded semiannually, is $14,008.93. Choice A is the best answer.

Question 12

Riverside Bank offers to lend you $50,000 at a nominal rate of 6.5%,compounded monthly.The loan (principal plus interest)must be repaid at the end of the year.Midwest Bank also offers to lend you the $50,000,but it will charge an annual rate of 6.2%,with no interest due until the end of the year.How much higher or lower is the effective annual rate charged by Midwest versus the rate charged by Riverside?

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Question 13

Suppose a bank offers to lend you $10,000 for 1 year on a loan contract that calls for you to make interest payments of $200.00 at the end of each quarter and then pay off the principal amount at the end of the year.What is the effective annual rate on the loan?

Accepted Answer

The effective annual rate (EAR) can be calculated by considering the quarterly interest payments and the principal repayment at the end of the year. The quarterly interest payment is $200, and there are four payments per year, totaling $800 in interest for the year on a $10,000 loan. However, to find the EAR, we must account for the compounding effect of the quarterly payments. The formula to calculate the EAR in this scenario, given the quarterly compounding, is: $$EAR = \left(1 + \frac{i}{n}\right)^n - 1$$ where $i$ is the annual interest rate and $n$ is the number of compounding periods per year. Since the question does not directly provide the annual interest rate but gives quarterly payments, we approach it by recognizing that the EAR reflects the equivalent annual interest rate considering compounding. The correct EAR, given the options, is 8.24%, which accounts for the compounding effect of making quarterly interest payments on the loan. This choice is derived from calculating the effective interest rate considering the structure of the payments, not from the simple interest calculation.

Question 14

You sold a car and accepted a note with the following cash flow stream as your payment.What was the effective price you received for the car assuming an interest rate of 13.0%? ​

Accepted Answer

To find the effective price received for the car, we need to calculate the present value of the cash flow stream using the given interest rate of 13.0%. Using a financial calculator or Excel, we find that the present value is $5,064. Therefore, the effective price received for the car is $5,064. Option B is the best choice.

Question 15

Charter Bank pays a 4.50% nominal rate on deposits,with monthly compounding.What effective annual rate (EFF%)does the bank pay?

Accepted Answer

The effective annual rate (EAR) can be calculated using the formula EAR = (1 + i/n)^(n*1) - 1, where i is the nominal interest rate and n is the number of compounding periods per year. For a 4.50% nominal rate with monthly compounding, EAR = (1 + 0.045/12)^(12*1) - 1 = 4.59%.

Question 16

What is the present value of the following cash flow stream at a rate of 11.00%? ​

Accepted Answer

Using a financial calculator or formula, the present value of the cash flow stream is calculated to be $447.80 at a rate of 11.00%.

Question 17

What is the present value of the following cash flow stream at a rate of 11.5%? ​

Accepted Answer

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Question 18

What's the present value of $1,375 discounted back 5 years if the appropriate interest rate is 6%,compounded monthly?

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Question 19

Assume that you own an annuity that will pay you $15,000 per year for 12 years,with the first payment being made today.You need money today to start a new business,and your uncle offers to give you $92,000 for the annuity.If you sell it,what rate of return would your uncle earn on his investment?

Accepted Answer

To calculate the rate of return that the uncle would earn from buying the annuity, we need to use the present value formula:
PV = C * (1 - (1 + r)^-n) / r
where PV is the present value of the annuity, C is the annual payment, r is the rate of return, and n is the number of years. We know that PV = $92,000, C = $15,000, and n = 12.

Using a financial calculator, we can solve for r:
92,000 = 15,000 * (1 - (1 + r)^-12) / r
r = 15.48%

Therefore, the uncle would earn a rate of return of 15.48% on his investment if he bought the annuity from you for $92,000. The correct answer is D.

Question 20

You are offered a chance to buy an asset for $5,250 that is expected to produce cash flows of $750 at the end of Year 1,$1,000 at the end of Year 2,$850 at the end of Year 3,and $6,250 at the end of Year 4.What rate of return would you earn if you bought this asset?

Accepted Answer

The rate of return can be calculated using the Net Present Value (NPV) formula set to zero, where the NPV equals the sum of the present values of all cash flows, including the initial investment. The correct rate of return is the one that makes the NPV equal to zero. By testing the given options or using financial calculator functions or software that solves for the internal rate of return (IRR), we find that option D, 16.91%, is the rate that accurately reflects the return on the investment given the cash flows and initial investment amount.

Quiz 5: Time Value of Money

What annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $2,600?

What's the future value of $4,500 after 5 years if the appropriate interest rate is 6%,compounded semiannually?

Your father paid $10,000 (CF at t = 0) for an investment that promises to pay $750 at the end of each of the next 5 years,then an additional lump sum payment of $11,500 at the end of the 5th year.What is the expected rate of return on this investment?

What's the future value of $1,600 after 5 years if the appropriate interest rate is 6%,compounded monthly?

What is the present value of the following cash flow stream at a rate of 13.5%?

Suppose your credit card issuer states that it charges a 23.75% nominal annual rate,but you must make monthly payments,which amounts to monthly compounding.What is the effective annual rate?

Master Card and other credit card issuers must by law print the Annual Percentage Rate (APR) on their monthly statements.If the APR is stated to be 19.25%,with interest paid monthly,what is the card's EFF%?

At a rate of 5.0%,what is the future value of the following cash flow stream?

Suppose Community Bank offers to lend you $10,000 for one year at a nominal annual rate of 19.50%,but you must make interest payments at the end of each quarter and then pay off the $10,000 principal amount at the end of the year.What is the effective annual rate on the loan?

Your girlfriend just won the Florida lottery.She has the choice of $10,800,000 today or a 20-year annuity of $1,050,000,with the first payment coming one year from today.What rate of return is built into the annuity? Disregard taxes.

What's the present value of $17,500 discounted back 5 years if the appropriate interest rate is 4.5%,compounded semiannually?

Suppose a bank offers to lend you $10,000 for 1 year on a loan contract that calls for you to make interest payments of $200.00 at the end of each quarter and then pay off the principal amount at the end of the year.What is the effective annual rate on the loan?

You sold a car and accepted a note with the following cash flow stream as your payment.What was the effective price you received for the car assuming an interest rate of 13.0%?

Charter Bank pays a 4.50% nominal rate on deposits,with monthly compounding.What effective annual rate (EFF%) does the bank pay?

What is the present value of the following cash flow stream at a rate of 11.00%?

What is the present value of the following cash flow stream at a rate of 11.5%?

What's the present value of $1,375 discounted back 5 years if the appropriate interest rate is 6%,compounded monthly?

Assume that you own an annuity that will pay you $15,000 per year for 12 years,with the first payment being made today.You need money today to start a new business,and your uncle offers to give you $92,000 for the annuity.If you sell it,what rate of return would your uncle earn on his investment?

You are offered a chance to buy an asset for $5,250 that is expected to produce cash flows of $750 at the end of Year 1,$1,000 at the end of Year 2,$850 at the end of Year 3,and $6,250 at the end of Year 4.What rate of return would you earn if you bought this asset?

Quiz 5: Time Value of Money

What annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $2,600?

What's the future value of $4,500 after 5 years if the appropriate interest rate is 6%,compounded semiannually?

Your father paid $10,000 (CF at t = 0) for an investment that promises to pay $750 at the end of each of the next 5 years,then an additional lump sum payment of $11,500 at the end of the 5th year.What is the expected rate of return on this investment?

What's the future value of $1,600 after 5 years if the appropriate interest rate is 6%,compounded monthly?

What is the present value of the following cash flow stream at a rate of 13.5%? ​

Suppose your credit card issuer states that it charges a 23.75% nominal annual rate,but you must make monthly payments,which amounts to monthly compounding.What is the effective annual rate?

Master Card and other credit card issuers must by law print the Annual Percentage Rate (APR) on their monthly statements.If the APR is stated to be 19.25%,with interest paid monthly,what is the card's EFF%?

At a rate of 5.0%,what is the future value of the following cash flow stream? ​

Suppose Community Bank offers to lend you $10,000 for one year at a nominal annual rate of 19.50%,but you must make interest payments at the end of each quarter and then pay off the $10,000 principal amount at the end of the year.What is the effective annual rate on the loan?

Your girlfriend just won the Florida lottery.She has the choice of $10,800,000 today or a 20-year annuity of $1,050,000,with the first payment coming one year from today.What rate of return is built into the annuity? Disregard taxes.

What's the present value of $17,500 discounted back 5 years if the appropriate interest rate is 4.5%,compounded semiannually?

Suppose a bank offers to lend you $10,000 for 1 year on a loan contract that calls for you to make interest payments of $200.00 at the end of each quarter and then pay off the principal amount at the end of the year.What is the effective annual rate on the loan?

You sold a car and accepted a note with the following cash flow stream as your payment.What was the effective price you received for the car assuming an interest rate of 13.0%? ​

Charter Bank pays a 4.50% nominal rate on deposits,with monthly compounding.What effective annual rate (EFF%) does the bank pay?

What is the present value of the following cash flow stream at a rate of 11.00%? ​

What is the present value of the following cash flow stream at a rate of 11.5%? ​

What's the present value of $1,375 discounted back 5 years if the appropriate interest rate is 6%,compounded monthly?

Assume that you own an annuity that will pay you $15,000 per year for 12 years,with the first payment being made today.You need money today to start a new business,and your uncle offers to give you $92,000 for the annuity.If you sell it,what rate of return would your uncle earn on his investment?

You are offered a chance to buy an asset for $5,250 that is expected to produce cash flows of $750 at the end of Year 1,$1,000 at the end of Year 2,$850 at the end of Year 3,and $6,250 at the end of Year 4.What rate of return would you earn if you bought this asset?

What is the present value of the following cash flow stream at a rate of 13.5%?

At a rate of 5.0%,what is the future value of the following cash flow stream?

You sold a car and accepted a note with the following cash flow stream as your payment.What was the effective price you received for the car assuming an interest rate of 13.0%?

What is the present value of the following cash flow stream at a rate of 11.00%?

What is the present value of the following cash flow stream at a rate of 11.5%?