Question 1

You are considering two loans.The terms of the two loans are equivalent with the exception of the interest rates.Loan A offers a rate of 7.75 percent,compounded daily.Loan B offers a rate of 8 percent,compounded semi-annually.Which loan should you select and why?

Accepted Answer

We can use the formula for calculating effective annual rates to compare the two loans.

For Loan A:
Effective Annual Rate = (1 + (0.0775/365))^365 - 1 = 0.0806 or 8.06%

For Loan B:
Effective Annual Rate = (1 + (0.08/2))^2 - 1 = 0.0816 or 8.16%

Since Loan A has a lower interest rate but is compounded more frequently, it ends up with a higher effective annual rate. Therefore, Loan A is the better choice.

Question 2

You are going to loan a friend $550 for one year at a 6 percent rate of interest,compounded annually.How much additional interest could you have earned if you had compounded the rate continuously rather than annually?

Accepted Answer

Additional interest = $550 × (0.0618365 - 0.06) = $1.01

Question 3

Your credit card company charges you 1.65 percent interest per month.What is the annual percentage rate on your account?

Accepted Answer

APR = 0.0165 × 12 = 19.80 percent

Question 4

You are paying an effective annual rate of 18.974 percent on your credit card.The interest is compounded monthly.What is the annual percentage rate on this account?

Accepted Answer

The annual percentage rate (APR) can be calculated from the effective annual rate (EAR) using the formula: EAR = (1 + APR/m)^m - 1, where m is the number of compounding periods per year. Given an EAR of 18.974% and monthly compounding (m = 12), we solve for APR. Rearranging the formula gives APR = m[(1 + EAR)^(1/m) - 1]. Plugging in the values, we find APR ≈ 17.50%.

Question 5

City Bank wants to appear competitive based on quoted loan rates and thus must offer a 7.75 percent annual percentage rate on its loans.What is the maximum rate the bank can actually earn based on the quoted rate?

Accepted Answer

The maximum rate the bank can actually earn based on the quoted rate is calculated by considering the effect of compounding. Since the quoted rate is 7.75 percent as an annual percentage rate (APR), if the bank compounds interest more frequently than annually, it can earn more than the quoted rate. The effective annual rate (EAR) can be calculated using the formula EAR = (1 + APR/n)^n - 1, where n is the number of compounding periods per year. To maximize the rate, the bank would compound as frequently as possible, theoretically an infinite number of times, leading to continuous compounding. Using continuous compounding, the formula becomes EAR = e^(APR) - 1, where e is the base of the natural logarithm, approximately 2.71828. However, without specifying the compounding frequency, we can't directly calculate the exact maximum rate. Among the given options, 8.06 percent is the closest to what could be achieved with frequent compounding (e.g., daily or monthly) without exceeding realistic banking practices. Therefore, without the exact compounding frequency or applying continuous compounding directly, we choose the option that represents a reasonable increase over the APR due to compounding.

Question 6

You just paid $750,000 for an annuity that will pay you and your heirs $42,000 a year forever.What rate of return are you earning on this policy?

Accepted Answer

The answer of You just paid $750,000 for an annuity...

Question 7

Wicker Imports established a trust fund that provides $90,000 in scholarships each year for needy students.The trust fund earns a fixed 6 percent rate of return.How much money did the firm contribute to the fund assuming that only the interest income is distributed?

Accepted Answer

To find the initial contribution to the fund, divide the annual scholarship amount by the interest rate: $90,000 / 0.06 = $1,500,000.

Question 8

You would like to establish a trust fund that will provide $120,000 a year forever for your heirs.The trust fund is going to be invested very conservatively so the expected rate of return is only 5.75 percent.How much money must you deposit today to fund this gift for your heirs?

Accepted Answer

To find the amount needed to deposit today to fund a perpetual annual payment, you can use the formula for the present value of a perpetuity: PV = PMT / r, where PV is the present value (the amount needed to deposit today), PMT is the annual payment ($120,000), and r is the annual interest rate (5.75% or 0.0575 as a decimal). Plugging in the values: PV = $120,000 / 0.0575 = $2,086,956.52, which rounds to $2,086,957.

Question 9

What is the effective annual rate of 5.25 percent compounded continuously?

Accepted Answer

The answer of What is the effective annual rate of...

Question 10

A preferred stock pays an annual dividend of $3.20.What is one share of this stock worth today if the rate of return is 11.75 percent?

Accepted Answer

The price of a preferred stock can be calculated using the dividend payment and the required rate of return.

Price of preferred stock = Dividend payment / Required rate of return

Price of preferred stock = $3.20 / 0.1175 = $27.23

Therefore, one share of this preferred stock is worth $27.23 today.

The correct answer is C.

Question 11

What is the annual percentage rate on a loan with a stated rate of 2.75 percent per quarter?

Accepted Answer

APR = 0.0275 × 4 = 11.00 percent

Question 12

The government has imposed a fine on the Corner Tavern.The fine calls for annual payments of $125,000,$100,000,$75,000,and $50,000,respectively,over the next four years.The first payment is due one year from today.The government plans to invest the funds until the final payment is collected and then donate the entire amount,including the investment earnings,to help the local community shelter.The government will earn 5.5 percent on the funds held.How much will the community shelter receive four years from today?

Accepted Answer

First, we need to calculate the future value of the payments and the interest earned on them. Using the formula:

FV = Payment * [(1 + r)^n - 1] / r

where r is the annual interest rate and n is the number of periods (in this case, 4), we get:

FV(125,000) = 530,266.08 
FV(100,000) = 424,212.86 
FV(75,000) = 318,159.63 
FV(50,000) = 212,106.41

Next, we add up these amounts to get the total future value:

Total FV = 1,484,745.98

Finally, we need to calculate the interest earned on this amount over four years at 5.5 percent:

Interest = Total FV * (1 + r)^n - Total FV 
= 164,764.01

The total amount the community shelter will receive in four years is:

Total = Total FV + Interest 
= 1,649,510.99

Therefore, the best choice is C ($392,510.99).

Question 13

You are borrowing money today at 8.48 percent,compounded annually.You will repay the principal plus all the interest in one lump sum of $12,800 two years from today.How much are you borrowing?

Accepted Answer

We can use the formula for compound interest:

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

Where:
A = the total amount at the end of the time period
P = the principal (amount borrowed)
r = the annual interest rate as a decimal
n = the number of times interest is compounded per year (in this case, once a year)
t = the time in years

We are given:
r = 8.48% = 0.0848
n = 1
t = 2
A = $12,800

Substituting these values into the formula:

$12,800 = P(1 + 0.0848/1)^(1*2)

Simplifying:

$12,800 = P(1.0848)^2

$12,800 = P(1.18099664)

P = $10,877.04

Therefore, the best choice is C.

Question 14

You grandfather won a lottery years ago.The value of his winnings at the time was $50,000.He invested this money such that it will provide annual payments of $2,400 a year to his heirs forever.What is the rate of return?

Accepted Answer

The rate of return can be found using the formula for the perpetuity: $ \text{Rate of Return} = \frac{\text{Annual Payment}}{\text{Principal}} $. Plugging in the given values: $ \text{Rate of Return} = \frac{2400}{50000} = 0.048 $ or 4.80 percent.

Question 15

What is the effective annual rate if a bank charges you 8.25 percent compounded quarterly?

Accepted Answer

To calculate the effective annual rate with quarterly compounding, we use the formula:
Effective Annual Rate = (1 + (nominal rate / number of compounding periods))^number of compounding periods - 1
Plugging in the values, we get:
Effective Annual Rate = (1 + (0.0825 / 4))^4 - 1
Effective Annual Rate = 0.0851 or 8.51 percent (rounded to two decimal places)
Therefore, the answer is D).

Question 16

What is the effective annual rate of 14.9 percent compounded continuously?

Accepted Answer

The answer of What is the effective annual rate of...

Question 17

You have $5,600 that you want to use to open a savings account.There are five banks located in your area.The rates paid by banks A through E,respectively,are given below.Which bank should you select if your goal is to maximize your interest income?

Accepted Answer

EAR_A = 4.61 percent Bank C offers the highest effective annual rate at 4.622 percent.

Question 18

The Pawn Shop loans money at an annual rate of 23 percent and compounds interest weekly.What is the actual rate being charged on these loans?

Accepted Answer

To find the actual rate being charged on these loans, we need to use the formula for calculating compound interest with a weekly compounding period:

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

where:
A = the balance after t periods
P = the principal amount
r = the annual interest rate (as a decimal)
n = the number of times per year that interest is compounded
t = the number of years

Plugging in the given values, we get:

A = P(1 + 0.23/52)^(52t)

To find the actual rate, we need to solve for r in the equation:

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

Since the loan is compounded weekly (n = 52), we get:

1 + r/52 = (A/P)^(1/52t)

r/52 = (A/P)^(1/52t) - 1

r = 52[(A/P)^(1/52t) - 1]

Let's assume that the loan is for one year, so t = 1. We can then calculate the actual rate as follows:

r = 52[(1 + 0.23/52)^(52*1) - 1] = 0.2580 or 25.80%

Therefore, the best choice is (B).

Question 19

The preferred stock of Casco has a 6.25 percent dividend yield.The stock is currently priced at $59.30 per share.What is the amount of the annual dividend?

Accepted Answer

C = $59.30 × 0.0625 = $3.71

Question 20

Your credit card company quotes you a rate of 17.9 percent.Interest is billed monthly.What is the actual rate of interest you are paying?

Accepted Answer

The actual rate of interest, also known as the effective annual rate (EAR), can be calculated when the nominal rate (quoted rate) and the number of compounding periods per year are known. In this case, with a nominal rate of 17.9% and monthly compounding (12 periods per year), the EAR can be calculated using the formula: $EAR = (1 + \frac{0.179}{12})^{12} - 1$. This calculation results in an EAR of approximately 19.44%, making option C the correct answer.

Quiz 6: Discounted Cash Flow Valuation