Question 1

Your uncle will sell you his bicycle shop for $250,000, with "seller financing," at a 6.0% nominal annual rate. The terms of the loan would require you to make 12 equal end-of-month payments per year for 4 years, and then make an additional final (balloon) payment of $50,000 at the end of the last month. What would your equal monthly payments be?
A) $4,029.37
B) $4,241.44
C) $4,464.67
D) $4,699.66
E) $4,947.01

Accepted Answer

The answer of Your uncle will sell you his bicycle...

Question 2

Your girlfriend just won the Florida lottery. She has the choice of $15,000,000 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?
A) 3.44%
B) 3.79%
C) 4.17%
D) 4.58%
E) 5.04%

Accepted Answer

The answer of Your girlfriend just won the Florida lottery....

Question 3

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 18.00%, with interest paid monthly, what is the card's EFF%?
A) 18.58%
B) 19.56%
C) 20.54%
D) 21.57%
E) 22.65%

Accepted Answer

The EFF% formula is (1+APR/m)^m - 1, where m is the number of compounding periods per year. Since interest is paid monthly, m = 12. Plugging in the numbers, we get (1+0.18/12)^12 - 1 = 0.1956 or 19.56% (rounded to the nearest hundredth). Therefore, the answer is B.

Question 4

Suppose Community Bank offers to lend you $10,000 for one year at a nominal annual rate of 8.00%, 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?
A) 8.24%
B) 8.45%
C) 8.66%
D) 8.88%
E) 9.10%

Accepted Answer

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Question 5

Charter Bank pays a 4.50% nominal rate on deposits, with monthly compounding. What effective annual rate (EFF%) does the bank pay?
A) 3.72%
B) 4.13%
C) 4.59%
D) 5.05%
E) 5.56%

Accepted Answer

To find the effective annual rate (EFF%), we use the following formula:

EFF% = (1 + (nominal rate/m))^m - 1

Where m is the number of compounding periods per year. In this case, m = 12 (monthly compounding).

EFF% = (1 + (0.045/12))^12 - 1 = 0.0459 or 4.59%

Therefore, the best choice is C.

Question 6

What annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $1,250?
A) $77.19
B) $81.25
C) $85.31
D) $89.58
E) $94.06

Accepted Answer

The formula for the present value of a perpetuity is:

PV = PMT / r

where PV is the present value, PMT is the annual payment, and r is the interest rate.

We are given that the perpetuity has a cost of $1,250, and we want to earn a rate of return of 6.5%.

So, we can set up the equation as:

$1,250 = PMT / 0.065

Solving for PMT, we get:

PMT = $81.25

Therefore, the annual payment we must receive in order to earn a 6.5% rate of return on this perpetuity is $81.25.

Question 7

What's the future value of $1,500 after 5 years if the appropriate interest rate is 6%, compounded semiannually?
A) $1,819
B) $1,915
C) $2,016
D) $2,117
E) $2,223

Accepted Answer

We can use the compound interest formula:

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

where FV is the future value, PV is the present value, r is the interest rate (as a decimal), n is the number of compounding periods per year, and t is the number of years.

Plugging in the given values, we get:

FV = 1500*(1 + 0.06/2)^(2*5)
FV = 1500*(1.03)^10
FV = 1500*1.344
FV = 2016

Therefore, the future value of $1,500 after 5 years with an interest rate of 6% compounded semiannually is $2,016.

The correct answer is C.

Question 8

Pace Co. borrowed $20,000 at a rate of 7.25%, simple interest, with interest paid at the end of each month. The bank uses a 360-day year. How much interest would Pace have to pay in a 30-day month?
A) $120.83
B) $126.88
C) $133.22
D) $139.88
E) $146.87

Accepted Answer

First, we need to calculate the daily interest rate:
7.25% / 360 = 0.02013888889 (rounded to 11 decimal places)

Then, we can calculate the interest for the 30-day month:
$20,000 x 0.02013888889 x 30 = $120.8333333

Rounding to the nearest cent gives us $120.83, which is choice (A).

Question 9

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 $250.00 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?
A) 8.46%
B) 8.90%
C) 9.37%
D) 9.86%
E) 10.38%

Accepted Answer

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Question 10

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 $120,000 for the annuity. If you sell it, what rate of return would your uncle earn on his investment?
A) 6.85%
B) 7.21%
C) 7.59%
D) 7.99%
E) 8.41%

Accepted Answer

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Question 11

What's the present value of $1,525 discounted back 5 years if the appropriate interest rate is 6%, compounded monthly?
A) $ 969
B) $1,020
C) $1,074
D) $1,131
E) $1,187

Accepted Answer

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Question 12

Suppose your credit card issuer states that it charges a 15.00% nominal annual rate, but you must make monthly payments, which amounts to monthly compounding. What is the effective annual rate?
A) 15.27%
B) 16.08%
C) 16.88%
D) 17.72%
E) 18.61%

Accepted Answer

The effective annual rate can be calculated using the formula: 
EAR = (1 + (r/m))^m - 1

Where r is the nominal annual rate and m is the number of compounding periods per year.

In this case, r = 15.00% and since there are 12 months in a year, m = 12.

Plugging into the formula: 
EAR = (1 + (0.15/12))^12 - 1 
EAR = 0.1608 or 16.08%

Therefore, the correct answer is B.

Question 13

What's the future value of $1,200 after 5 years if the appropriate interest rate is 6%, compounded monthly?
A) $1,537.69
B) $1,618.62
C) $1,699.55
D) $1,784.53
E) $1,873.76

Accepted Answer

We can use the formula A=P(1+r/n)^(nt), where A is the future value, P is the initial principal, r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years. Plugging in the values, we get A=1200(1+0.06/12)^(12*5)=1618.62, which is closest to option B.

Question 14

Suppose you are buying your first condo for $145,000, and you will make a $15,000 down payment. You have arranged to finance the remainder with a 30-year, monthly payment, amortized mortgage at a 6.5% nominal interest rate, with the first payment due in one month. What will your monthly payments be?
A) $741.57
B) $780.60
C) $821.69
D) $862.77
E) $905.91

Accepted Answer

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Question 15

Suppose you deposited $5,000 in a bank account that pays 5.25% with daily compounding based on a 360-day year. How much would be in the account after 8 months, assuming each month has 30 days?
A) $5,178.09
B) $5,436.99
C) $5,708.84
D) $5,994.28
E) $6,294.00

Accepted Answer

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. In this case, P = $5,000, r = 5.25% or 0.0525, n = 360 (daily compounding), and t = 8/12 years (since 8 months is 8/12 of a year). Plugging these values into the formula gives A = 5000(1 + 0.0525/360)^(360*(8/12)), which calculates to approximately $5,178.09.

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 $10,000 at the end of the 5th year. What is the expected rate of return on this investment?
A) 6.77%
B) 7.13%
C) 7.50%
D) 7.88%
E) 8.27%

Accepted Answer

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Question 17

You are offered a chance to buy an asset for $7,250 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?
A) 4.93%
B) 5.19%
C) 5.46%
D) 5.75%
E) 6.05%

Accepted Answer

The rate of return can be calculated using the Net Present Value (NPV) formula set to zero, because the NPV of investing in the asset should equal the cost of the investment for the investor to earn the expected rate of return. The cash flows are discounted back at the rate of return to find the present value, which should equal the investment cost of $7,250. The correct rate of return is the one that makes the NPV equal to zero. Through financial calculation or using a financial calculator, the rate that fits this criterion is 6.05%.

Question 18

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 7.0%, 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?
A) 0.52%
B) 0.44%
C) 0.36%
D) 0.30%
E) 0.24%

Accepted Answer

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Question 19

Suppose you borrowed $12,000 at a rate of 9.0% and must repay it in 4 equal installments at the end of each of the next 4 years. How large would your payments be?
A) $3,704.02
B) $3,889.23
C) $4,083.69
D) $4,287.87
E) $4,502.26

Accepted Answer

This is a problem of calculating the payment for an installment loan, which can be solved using the formula for the annuity payment or an amortization calculator. Given a principal of $12,000, an annual interest rate of 9.0%, and a term of 4 years, the correct payment amount is $3,704.02. This calculation takes into account the interest on the declining balance over the period, ensuring that both the principal and the interest are fully paid off over the 4 years.

Question 20

What's the present value of $4,500 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually?
A) $3,089
B) $3,251
C) $3,422
D) $3,602
E) $3,782

Accepted Answer

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Quiz 5: Time Value of Money

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

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 18.00%, with interest paid monthly, what is the card's EFF%?

Suppose Community Bank offers to lend you $10,000 for one year at a nominal annual rate of 8.00%, 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?

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

What annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $1,250?

What's the future value of $1,500 after 5 years if the appropriate interest rate is 6%, compounded semiannually?

Pace Co. borrowed $20,000 at a rate of 7.25%, simple interest, with interest paid at the end of each month. The bank uses a 360-day year. How much interest would Pace have to pay in a 30-day month?

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 $250.00 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 present value of $1,525 discounted back 5 years if the appropriate interest rate is 6%, compounded monthly?

Suppose your credit card issuer states that it charges a 15.00% nominal annual rate, but you must make monthly payments, which amounts to monthly compounding. What is the effective annual rate?

What's the future value of $1,200 after 5 years if the appropriate interest rate is 6%, compounded monthly?

Suppose you deposited $5,000 in a bank account that pays 5.25% with daily compounding based on a 360-day year. How much would be in the account after 8 months, assuming each month has 30 days?

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 $10,000 at the end of the 5th year. What is the expected rate of return on this investment?

You are offered a chance to buy an asset for $7,250 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?

Suppose you borrowed $12,000 at a rate of 9.0% and must repay it in 4 equal installments at the end of each of the next 4 years. How large would your payments be?

What's the present value of $4,500 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually?