Question 1

Downtown Bank is offering 2.2 percent compounded daily on its savings accounts.You deposit $8,000 today.How much will you have in your account 11 years from now?

Accepted Answer

FV = $8,000 × [1 + (0.022/365)]¹¹ ^{× 365} = $10,190.28

Question 2

You need a 30-year, fixed-rate mortgage to buy a new home for $240,000.Your mortgage bank will lend you the money at a 7.5 percent APR for this 360-month loan, with interest compounded monthly.However, you can only afford monthly payments of $850, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment.What will be the amount of the balloon payment if you are to keep your monthly payments at $850?

Accepted Answer

Remaining principal = $240,000 - $121,564.98 = $118,435.02Balloon payment = $118,435.02 × [1 + (0.075/12)]³⁰ ^{× 12} = $1,115,840

Question 3

You have just won the lottery and will receive $540,000 as your first payment one year from now.You will receive payments for 26 years.The payments will increase in value by 4 percent each year.The appropriate discount rate is 10 percent.What is the present value of your winnings?

Accepted Answer

The present value of the winnings can be calculated using the formula for the present value of a growing annuity. The formula is: PV = P * [(1 - (1 + g)^n / (1 + r)^n) / (r - g)], where P is the first payment, g is the growth rate, n is the number of payments, and r is the discount rate. Plugging in the values: P = $540,000, g = 4% or 0.04, n = 26, and r = 10% or 0.10, we get the present value of the winnings. Calculating with these inputs gives a present value of approximately $6,906,372, which matches option B.

Question 4

On the day you entered college you borrowed $30,000 from your local bank.The terms of the loan include an interest rate of 4.75 percent.The terms stipulate that the principal is due in full one year after you graduate.Interest is to be paid annually at the end of each year.Assume that you complete college in four years.How much total interest will you pay on this loan?

Accepted Answer

To calculate the total interest, we need to first calculate the annual interest and then multiply it by the number of years we will be paying. 
Annual interest = $30,000 * 4.75% = $1,425 
Total interest for 4 years = $1,425 * 4 = $5,700 
However, we also need to add the interest due at the end of the fourth year, which is calculated as follows: 
Interest for year 4 = $30,000 * 4.75% = $1,425 
Total interest = $5,700 + $1,425 = $7,125

Therefore, the correct answer is C.

Question 5

You just acquired a mortgage in the amount of $249,500 at 6.75 percent interest, compounded monthly.Equal payments are to be made at the end of each month for thirty years.How much of the first loan payment is interest? (Assume each month is equal to 1/12 of a year.)

Accepted Answer

The answer of You just acquired a mortgage in the...

Question 6

You are planning to save for retirement over the next 15 years.To do this, you will invest $1,100 a month in a stock account and $500 a month in a bond account.The return on the stock account is expected to be 7 percent, and the bond account will pay 4 percent.When you retire, you will combine your money into an account with a 5 percent return.How much can you withdraw each month during retirement assuming a 20-year withdrawal period?

Accepted Answer

The answer of You are planning to save for retirement...

Question 7

You want to be a millionaire when you retire in 40 years.You can earn A 12.5 percent annual return.How much more will you have to save each month if you wait 10 years to start saving versus if you start saving at the end of this month?

Accepted Answer

FVA_{40 years} = $1,000,000 = C × [{[1 + (0.125/12)]⁴⁰ ^{× 12}; C = $72.53FVA_{30 years} = $1,000,000 = C × [{[1 + (0.125/12)]³⁰ ^{× 12}; C = $255.91Difference = $255.91 - $72.53 = $183.38

Question 8

First Century Bank wants to earn an effective annual return on its consumer loans of 10 percent per year.The bank uses daily compounding on its loans.By law, what interest rate is the bank required to report to potential borrowers?

Accepted Answer

APR = 365 × [(1 + 0.10)^1/365 - 1] = 9.53 percent

Question 9

On June 1, you borrowed $220,000 to buy a house.The mortgage rate is 8.25 percent.The loan is to be repaid in equal monthly payments over 15 years.The first payment is due on July 1.How much of the second payment applies to the principal balance? (Assume that each month is equal to 1/12 of a year.)

Accepted Answer

The answer of On June 1, you borrowed $220,000 to...

Question 10

Consider a firm with a contract to sell an asset 3 years from now for $90,000.The asset costs $71,000 to produce today.At what rate will the firm just break even on this contract?

Accepted Answer

To break even on the contract, the firm needs to earn an interest rate that compensates it for the cost of capital of producing the asset. We can use the following equation to solve for the interest rate:

$71,000 x (1 + r)^3 = $90,000

Simplifying the equation, we get:

(1 + r)^3 = $90,000/$71,000
(1 + r)^3 = 1.2676
1 + r = 1.2676^(1/3)
1 + r = 1.0823
r = 1.0823 - 1
r = 0.0823

Therefore, the firm needs to earn an interest rate of 8.23 percent to break even on the contract. The answer is C.

Question 11

This morning, you borrowed $150,000 to buy a house.The mortgage rate is 7.35 percent.The loan is to be repaid in equal monthly payments over 20 years.The first payment is due one month from today.How much of the second payment applies to the principal balance? (Assume that each month is equal to 1/12 of a year.)

Accepted Answer

The monthly interest rate is 7.35%/12 = 0.6125%. 
The number of months for 20 years is 20 ×12 = 240. 
The monthly payment, using the formula for a mortgage, is:
P = (rPv)/(1-(1+r)^-n), where r is the monthly interest rate, P is the loan amount, and n is the total number of months.
P = (0.006125×150000)/(1-(1+0.006125)^-240) = $1,060.66
To find out how much of the monthly payment goes towards interest, we multiply the monthly interest rate by the current balance (which is the original balance minus the cumulative principal payments).
So for the first payment, the interest portion is: 0.006125 × $150,000 = $918.75
The remaining portion of the payment (i.e. the difference between the monthly payment and the interest portion) goes towards the principal repayment.
So the principal repayment for the first month is $1,060.66 - $918.75= $141.91
To find out how much of the second payment applies to the principal balance, we subtract the interest portion of the second payment from the monthly payment, and then subtract this amount from the principal balance remaining after the first payment.
The interest portion of the second payment is: 0.006125 × ($150,000 - $141.91) = $535.98
So the amount of the second payment that applies to the principal balance is: $1,060.66 - $535.98 = $524.68
Therefore, the correct answer is B) $277.61

Question 12

You want to buy a new sports coupe for $41,750, and the finance office at the dealership has quoted you an 8.6 percent APR loan compounded monthly for 48 months to buy the car.What is the effective interest rate on this loan?

Accepted Answer

EAR = [1 + (.086/12)]¹² - 1 = 8.95 percent

Question 13

Western Bank offers you a $21,000, 9-year term loan at 8 percent annual interest.What is the amount of your annual loan payment?

Accepted Answer

We can use the formula:

Annual Payment = (Loan Amount x Annual Interest Rate) / (1 - (1 + Annual Interest Rate)^(-Number of Years))

Plugging in the values, we get:

Annual Payment = (21,000 x 0.08) / (1 - (1 + 0.08)^(-9)) = $3,361.67

Therefore, the best choice is B.

Question 14

The present value of the following cash flow stream is $5,933.86 when discounted at 11 percent annually.What is the value of the missing cash flow?

Accepted Answer

The answer of The present value of the following cash...

Question 15

You want to borrow $47,170 from your local bank to buy a new sailboat.You can afford to make monthly payments of $1,160, but no more.Assume monthly compounding.What is the highest rate you can afford on a 48-month APR loan?

Accepted Answer

The answer of You want to borrow $47,170 from your...

Question 16

You are preparing to make monthly payments of $72, beginning at the end of this month, into an account that pays 6 percent interest compounded monthly.How many payments will you have made when your account balance reaches $9,312?

Accepted Answer

t = ln 1.6467/ln 1.005; t = 100 payments

Question 17

What is the present value of $1,100 per year, at a discount rate of 10 percent if the first payment is received 6 years from now and the last payment is received 30 years from now?

Accepted Answer

We can use the formula for the present value of an annuity:

$PV = \dfrac{C[(1 + r)^n - (1 + r)^{-m}]}{r}$

Where:
C = the annual payment
n = the number of periods in total
m = the number of periods from the first payment to the present
r = the discount rate

Plugging in the values from the problem, we get:

$PV = \dfrac{1100[(1 + 0.10)^{25} - (1 + 0.10)^{-5}]}{0.10}$
$PV = 6199.74$

Therefore, the present value is $6,199.74, which is closest to choice A.

Question 18

Beginning three months from now, you want to be able to withdraw $1,700 each quarter from your bank account to cover college expenses over the next 4 years.The account pays 1.25 percent interest per quarter.How much do you need to have in your account today to meet your expense needs over the next 4 years?

Accepted Answer

To solve this, we use the formula for the present value of an annuity: $PV = PMT \times \left[\frac{1 - (1 + r)^{-n}}{r}\right]$, where PMT is the payment amount per period, r is the interest rate per period, and n is the total number of payments. Here, PMT = $1,700, r = 0.0125 (1.25%), and n = 4 years * 4 quarters/year = 16 quarters. Plugging these values into the formula gives: $PV = 1700 \times \left[\frac{1 - (1 + 0.0125)^{-16}}{0.0125}\right] = $24,514.50$.

Question 19

On the day you entered college, you borrowed $18,000 on an interest-only, four-year loan at 5.25 percent from your local bank.Payments are to be paid annually.What is the amount of your loan payment in year 2?

Accepted Answer

Payment in year 2 = $18,000 × 0.0525 = $945

Question 20

You have just purchased a new warehouse.To finance the purchase, you've arranged for a 30-year mortgage loan for 80 percent of the $2,600,000 purchase price.The monthly payment on this loan will be $12,200.What is the effective annual rate on this loan?

Accepted Answer

Loan amount = $2,600,000 × 0.80 = $2,080,000 EAR = [1 + (.05797/12)]¹² - 1 = 5.95 percent

Quiz 6: Bond Valuation