Question 1

Suppose your credit card issuer states that it charges a 19.50% 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 use the formula:

(1 + r/n)^n - 1

where r is the nominal annual rate and n is the number of times the interest is compounded per year.

In this case, r = 19.50% and n = 12 (since there are 12 months in a year).

Plugging in the numbers, we get:

(1 + 0.1950/12)^12 - 1 = 0.2134 or 21.34%

Therefore, the effective annual rate is 21.34%.

Question 2

Your girlfriend just won the Florida lottery.She has the choice of $15,900,000 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.

Accepted Answer

The rate of return built into the annuity can be calculated using the present value of an annuity formula. Solving for the interest rate that equates the present value of the annuity payments ($1,050,000 per year for 20 years) to the lump sum amount ($15,900,000) gives approximately 2.81%.

Question 3

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 7.0%?  ​

Accepted Answer

To find the effective price received for the car, we need to find the present value of the cash flow stream using the given interest rate of 7%. Using a financial calculator, we get the present value to be $5,840, which is the effective price received for the car.

Question 4

What annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $1,600?

Accepted Answer

The answer of What annual payment must you receive in...

Question 5

What is the present value of the following cash flow stream at a rate of 10.0%?  ​

Accepted Answer

The answer of What is the present value of the...

Question 6

Charter Bank pays a 5.00% nominal rate on deposits,with monthly compounding.What effective annual rate (EFF%)does the bank pay?

Accepted Answer

The formula for calculating the effective annual rate (EFF%) with monthly compounding is:

EFF% = (1 + (nominal interest rate / number of compounding periods))^number of compounding periods - 1

Plugging in the values given:

EFF% = (1 + (0.05 / 12))^12 - 1
EFF% = (1.004167)^12 - 1
EFF% = 0.051161 or 5.12%

Therefore, the correct answer is A) 5.12%.

Question 7

What is the present value of the following cash flow stream at a rate of 10.0%?  ​

Accepted Answer

The answer of What is the present value of the...

Question 8

At a rate of 5.5%,what is the future value of the following cash flow stream?  ​

Accepted Answer

The answer of At a rate of 5.5%,what is the...

Question 9

What is the present value of the following cash flow stream at a rate of 7.00%?  ​

Accepted Answer

Using a financial calculator or Excel, the present value of the cash flow stream can be calculated as the sum of the present values of each individual cash flow. Alternatively, the present value of an annuity formula can be used to calculate the present value of the cash flow stream as a whole. Using the latter method, the present value can be calculated as follows:

PV = C[(1 - (1+r)^-n)/r] 
PV = 50[(1 - (1+0.07)^-5)/0.07] + 75[(1 - (1+0.07)^-6)/0.07] + 100[(1 - (1+0.07)^-7)/0.07] + 225[(1 - (1+0.07)^-8)/0.07]
PV = $495.49

Therefore, the best choice is (C) $495.49.

Question 10

Suppose Community Bank offers to lend you $10,000 for one year at a nominal annual rate of 17.75%,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?

Accepted Answer

The answer of Suppose Community Bank offers to lend you...

Question 11

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 $170.00 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 using the formula for the nominal interest rate compounded quarterly. The nominal rate is $170 per quarter on a $10,000 loan, which is 1.7% per quarter. The EAR is calculated as (1 + 0.017)^4 - 1 = 0.0698 or 6.98%.

Question 12

What's the future value of $3,300 after 5 years if the appropriate interest rate is 6%,compounded semiannually?

Accepted Answer

The formula for future value with semiannual compounding is FV = P(1 + r/2)^2n, where P is the present value, r is the interest rate (as a decimal), and n is the number of semiannual periods. Plugging in the values, we get FV = 3300(1 + 0.06/2)^(2*5) = $4,434.92, rounded to the nearest cent. Therefore, the best choice is B.

Question 13

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?

Accepted Answer

The answer of Riverside Bank offers to lend you $50,000...

Question 14

What's the present value of $1,700 discounted back 5 years if the appropriate interest rate is 6%,compounded monthly?

Accepted Answer

The present value (PV) is calculated using the formula: PV = FV / (1 + r/n)^(nt), where FV is the future value ($1,700), r is the annual interest rate (0.06), n is the number of compounding periods per year (12), and t is the number of years (5). Plugging in these values gives PV = 1700 / (1 + 0.06/12)^(12*5) = $1,260.33.

Question 15

You are offered a chance to buy an asset for $4,500 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 answer of You are offered a chance to buy...

Question 16

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 $17,750 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 calculated by finding 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 18.27%.

Question 17

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 24.25%,with interest paid monthly,what is the card's EFF%?

Accepted Answer

The formula to convert APR to EFF% with interest paid monthly is:
EFF% = (1 + APR/12)^12 - 1
Plugging in the values, we get:
EFF% = (1 + 24.25%/12)^12 - 1
EFF% = 27.14%
Therefore, the answer is A) 27.14%.

Question 18

What's the future value of $1,950 after 5 years if the appropriate interest rate is 6%,compounded monthly?

Accepted Answer

The future value is calculated using the formula FV = P(1 + r/n)^(nt), where P is the principal amount ($1,950), r is the annual interest rate (0.06), n is the number of times interest is compounded per year (12), and t is the number of years (5). Plugging in these values gives FV = 1950(1 + 0.06/12)^(12*5) = $2,630.26.

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 $156,000 for the annuity.If you sell it,what rate of return would your uncle earn on his investment?

Accepted Answer

The correct answer is D.The present value of the annuity can be calculated using the formula:PV = PMT * [1 - (1 + r)^-n] / rwhere:PV is the present valuePMT is the annual paymentr is the annual interest raten is the number of yearsIn this case, PMT = $15,000, n = 12, and PV = $156,000. Solving for r, we get:r = 2.72%

Question 20

What's the present value of $11,500 discounted back 5 years if the appropriate interest rate is 4.5%,compounded semiannually?

Accepted Answer

We use the formula PV = FV/(1+r/m)^(m*t) where PV is present value, FV is future value, r is the annual interest rate, m is the number of compounding periods per year, and t is the number of years. Plugging in the values, we get PV = 11,500/(1+(0.045/2))^(2*5) = $9,205.87. Therefore, the best choice is A.

Quiz 5: Time Value of Money

Suppose your credit card issuer states that it charges a 19.50% nominal annual rate,but you must make monthly payments,which amounts to monthly compounding.What is the effective annual rate?

Your girlfriend just won the Florida lottery.She has the choice of $15,900,000 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.

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 7.0%?

What annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $1,600?

What is the present value of the following cash flow stream at a rate of 10.0%?

Charter Bank pays a 5.00% 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 10.0%?

At a rate of 5.5%,what is the future value of the following cash flow stream?

What is the present value of the following cash flow stream at a rate of 7.00%?

Suppose Community Bank offers to lend you $10,000 for one year at a nominal annual rate of 17.75%,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?

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 $170.00 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?

What's the future value of $3,300 after 5 years if the appropriate interest rate is 6%,compounded semiannually?

What's the present value of $1,700 discounted back 5 years if the appropriate interest rate is 6%,compounded monthly?

You are offered a chance to buy an asset for $4,500 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?

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 $17,750 at the end of the 5th year.What is the expected rate of return on this investment?

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 24.25%,with interest paid monthly,what is the card's EFF%?

What's the future value of $1,950 after 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 $156,000 for the annuity.If you sell it,what rate of return would your uncle earn on his investment?

What's the present value of $11,500 discounted back 5 years if the appropriate interest rate is 4.5%,compounded semiannually?

Quiz 5: Time Value of Money

Suppose your credit card issuer states that it charges a 19.50% nominal annual rate,but you must make monthly payments,which amounts to monthly compounding.What is the effective annual rate?

Your girlfriend just won the Florida lottery.She has the choice of $15,900,000 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.

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 7.0%? ​

What annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $1,600?

What is the present value of the following cash flow stream at a rate of 10.0%? ​

Charter Bank pays a 5.00% 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 10.0%? ​

At a rate of 5.5%,what is the future value of the following cash flow stream? ​

What is the present value of the following cash flow stream at a rate of 7.00%? ​

Suppose Community Bank offers to lend you $10,000 for one year at a nominal annual rate of 17.75%,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?

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 $170.00 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?

What's the future value of $3,300 after 5 years if the appropriate interest rate is 6%,compounded semiannually?

What's the present value of $1,700 discounted back 5 years if the appropriate interest rate is 6%,compounded monthly?

You are offered a chance to buy an asset for $4,500 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?

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 $17,750 at the end of the 5th year.What is the expected rate of return on this investment?

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 24.25%,with interest paid monthly,what is the card's EFF%?

What's the future value of $1,950 after 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 $156,000 for the annuity.If you sell it,what rate of return would your uncle earn on his investment?

What's the present value of $11,500 discounted back 5 years if the appropriate interest rate is 4.5%,compounded semiannually?

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 7.0%?

What is the present value of the following cash flow stream at a rate of 10.0%?

What is the present value of the following cash flow stream at a rate of 10.0%?

At a rate of 5.5%,what is the future value of the following cash flow stream?

What is the present value of the following cash flow stream at a rate of 7.00%?