Question 1

To compare interest rates,we should compare the

Accepted Answer

Effective rates take into account the compounding of interest over a specific period of time, giving us a more accurate representation of the true cost of borrowing or the true earnings from saving. Quoted rates may not account for compounding, nominal rates only state the interest rate without factoring in compounding, and periodic rates may not reflect the true cost or earnings over the life of the loan or investment.

Question 2

The R&M Bank has offered you the choice between two loans:
#1 charges interest at a rate of 9% compounded quarterly.
#2 charges interest at a rate of 9.50% compounded semi-annually.
Which loan do you prefer and why?

Accepted Answer

Loan #1 has a lower effective interest rate when calculated as it compounds more frequently (quarterly) compared to Loan #2 (semi-annually).

Question 3

Your credit card has a quoted rate of 18.5 percent compounded daily.What is the effective annual rate? (Assume 360 days a year.)

Accepted Answer

The effective annual rate (EAR) can be calculated using the formula: EAR = (1 + i/n)^(n*t) - 1, where i is the nominal rate (0.185), n is the number of compounding periods per year (360), and t is the time in years (1). Plugging in the values, EAR = (1 + 0.185/360)^(360*1) - 1 ≈ 0.2032 or 20.32%.

Question 4

For a given effective annual rate,the quoted rate ______ as the compounding frequency increases.

Accepted Answer

The answer of For a given effective annual rate,the quoted...

Question 5

The R&M Bank has offered you the choice between two investment accounts:
#1 pays interest at a rate of 12% compounded semi-annually.
#2 pays interest at a rate of 11% compounded monthly.
Which investment account do you prefer and why?

Accepted Answer

Account #1 has a higher effective annual rate (EAR) due to the higher nominal rate, despite the less frequent compounding compared to account #2.

Question 6

For a given quoted rate,the effective annual rate ______ as the compounding frequency increases.

Accepted Answer

The effective annual rate increases as the compounding frequency increases because more compounding leads to a higher total interest earned over the year.

Question 7

In 30 years,you plan to set up a fellowship fund for your university that pays out $100,000/year in perpetuity with an annually compounded discount rate of 5%.In order to set up the fund in 30 years,how much do you need to save each year (starting this year)assuming you can get a semi-annually compounded return of 10% on your savings for the next 30 years?

Accepted Answer

First, we need to calculate the present value of the perpetuity that will be created in 30 years. Using the perpetuity formula, we get:

PV = Payment / Discount rate
PV = $100,000 / 5%
PV = $2,000,000

Next, we need to calculate the amount we need to save each year to reach $2,000,000 in 30 years. We can use the annuity formula for this:

PV = Payment x (1 - (1 + r/n)^(-nt)) / (r/n)
$2,000,000 = Payment x (1 - (1 + 10%/2)^(-2*30)) / (10%/2)
$2,000,000 = Payment x 34.67584008

Payment = $57,750.72

Therefore, we need to save $57,750.72 each year for the next 30 years to reach our target of $2,000,000.

Question 8

The R&M Bank currently offers an investment account with an interest rate of 8% compounded semi-annually.R&M wants to offer customers another account with interest compounded monthly.If R&M wants the effective rates to be equal,what interest rate should R&M quote for the second account?

Accepted Answer

The answer of The R&M Bank currently offers an investment...

Question 9

Your credit card has a quoted rate of 17% compounded weekly.What is the effective annual rate?

Accepted Answer

The effective annual rate (EAR) can be calculated using the formula EAR = (1 + i/n)^(n*1) - 1, where i is the annual interest rate and n is the number of compounding periods per year. For a 17% rate compounded weekly, i = 0.17 and n = 52. Plugging these into the formula gives EAR = (1 + 0.17/52)^(52*1) - 1 ≈ 0.1850 or 18.50%.

Question 10

Which one of the following will increase the present value of an annuity?

Accepted Answer

Lowering the discount rate will decrease the rate at which future cash flows are discounted back to their present value, resulting in a higher present value for the annuity.

Question 11

An annuity due pays out

Accepted Answer

An annuity due is a financial instrument in which a fixed amount of money is paid at the beginning of each time period for a fixed number of periods. Therefore, choice C is the correct answer. The other options do not accurately describe an annuity due.

Question 12

A pension fund pays out $50,000 a year in perpetuity,based on a cost of capital of 5%,to retiring employees.Alternatively,the employee can take out a lump sum of $1 million payable immediately.The employee should choose

Accepted Answer

The answer of A pension fund pays out $50,000 a...

Question 13

Eloise has deposited $2,000 in an investment account that pays 5% compounded continuously.How much will she have in her account in two years?

Accepted Answer

The formula for continuous compounding is given by:

A = Pe^(rt)

Where:
A = Amount
P = Principal (initial deposit)
e = Euler's number (approximately 2.71828)
r = Rate of interest (in decimal form)
t = Time

Plugging in the given values, we get:

A = 2000 e^(0.05*2)
A = 2000 e^(0.1)
A = 2000 * 1.10517091807
A = 2210.34

So Eloise will have $2,210.34 in her account after two years.

Thus, the best choice is B.

Question 14

Your investment account pays interest at a rate of 8% compounded semi-annually.If you deposit $1,000 today,how much will you have in two years?

Accepted Answer

Using the formula for compound interest: 
A = P(1 + r/n)^(nt)
where 
A = final amount 
P = principal (initial amount)
r = annual interest rate 
n = number of times the interest is compounded per year 
t = time in years

Plugging in the given values, we get:
A = 1000(1 + 0.08/2)^(2*2)
A = 1000(1 + 0.04)^4
A = 1000(1.04)^4
A = 1169.86

Therefore, after two years, you will have $1,169.86 in your investment account.

Question 15

How much should a monthly compounded account with an EAR of 10% earn semi-annually?

Accepted Answer

The answer of How much should a monthly compounded account...

Question 16

Valentino will receive $25,000 in 3 years.His opportunity cost is 8% compounded continuously.The present value of this cash flow is closest to

Accepted Answer

The answer of Valentino will receive $25,000 in 3 years.His...

Question 17

Wilma borrows $10,000 from "Jaw Breaker Joe" and promises to repay Joe a total of $10,500 in one month.What is the effective annual interest rate charged by Joe?

Accepted Answer

To find the effective annual interest rate, we need to use the formula:

Effective annual interest rate = [(1 + periodic interest rate)^n - 1] x 100%

Where:

Periodic interest rate = (total repayment amount - principal amount) / principal amount = ($10,500 - $10,000) / $10,000 = 5%
n = number of periods in a year = 12 (since we have a monthly repayment schedule)

Plugging these values into the formula, we get:

Effective annual interest rate = [(1 + 5%)^12 - 1] x 100% ≈ 79.59%

Therefore, the effective annual interest rate charged by Joe is 79.59%. The answer is C.

Question 18

Your investment account has an interest rate of 10% compounded semi-annually.This is the equivalent of an effective annual interest rate of

Accepted Answer

To find the effective annual interest rate, we need to use the formula:

Effective annual interest rate = (1 + (nominal interest rate/n))^n - 1

where n is the number of compounding periods per year. In this case, the nominal interest rate is 10% and there are two compounding periods per year (semi-annually), so:

Effective annual interest rate = (1 + (0.1/2))^2 - 1
= (1.05)^2 - 1
= 1.1025 - 1
= 0.1025 or 10.25%

Therefore, the best choice is D, 10.25%.

Question 19

You have been offered four different financing schemes for a $30,000 car.Which one should you choose?

Accepted Answer

The monthly payment is lower than the other options.

Question 20

Which of the following is the most appropriate timeline for the cash flows of a three-year annuity due with annual cash flows of $5,000?

Accepted Answer

For a three-year annuity due with annual cash flows of $5,000, the cash flows occur at the beginning of each year. Therefore, the cash flows would be as follows: Year 1 - $5,000; Year 2 - $5,000; Year 3 - $5,000. The timeline that depicts this is option B.

Quiz 5: Time Value of Money