Question 1

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 2

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 for calculating the annual loan payment, which is:

Annual Payment = (Loan Amount / Present Value Factor) x Payment Factor

The Present Value Factor and Payment Factor can be found in a loan amortization table or using financial calculators.

For a $21,000 loan at 8% annual interest for 9 years, the Present Value Factor is 7.0366 and the Payment Factor is 0.052232.

Plugging in the values, we get:

Annual Payment = (21,000 / 7.0366) x 0.052232
Annual Payment = 3,361.67

Therefore, the best choice is B, with an annual loan payment of $3,361.67.

Question 3

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 4

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

PV of missing cash flow = $5,933.86 - ($2,000/1.11) - ($1,750/1.11³) - ($1,250/1.11⁴) = $2,029.06CF₂ = $2,029.06 × 1.11² = $2,500

Question 5

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 6

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 7

This morning,you borrowed $9,500 at 8.9 percent annual interest.You are to repay the loan principal plus all of the loan interest in one lump sum four years from today.How much will you have to repay?

Accepted Answer

The answer of This morning,you borrowed $9,500 at 8.9 percent...

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

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 10

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 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

To find how much of the second payment applies to the principal balance, we first need to calculate the monthly payment amount using the loan amount, interest rate, and loan term. The formula for the monthly payment (M) on a fixed-rate mortgage is:$$M = P \frac{r(1+r)^n}{(1+r)^n - 1}$$where:- $P$ is the loan amount ($150,000),- $r$ is the monthly interest rate (annual rate divided by 12, so 7.35% / 12 = 0.06125 or 0.006125 as a decimal),- $n$ is the total number of payments (20 years * 12 months = 240).Plugging in the numbers:$$M = 150,000 \frac{0.006125(1+0.006125)^{240}}{(1+0.006125)^{240} - 1}$$$$M \approx 1,194.67$$This is the total monthly payment. To find out how much of the second payment applies to the principal, we need to calculate the interest portion of the first payment and subtract it from the total monthly payment to see how much of the first payment goes towards the principal. Then, we calculate the interest for the second month based on the reduced principal and subtract this new interest from the total monthly payment to find the principal portion of the second payment.Interest for the first month:$$Interest = Principal \times monthly\ rate = 150,000 \times 0.006125 = 917.50$$Principal portion of the first payment:$$Principal\ portion = Total\ monthly\ payment - Interest = 1,194.67 - 917.50 = 277.17$$After the first payment, the new principal balance is:$$New\ principal = Original\ principal - Principal\ portion\ of\ first\ payment = 150,000 - 277.17 = 149,722.83$$Interest for the second month:$$Interest = New\ principal \times monthly\ rate = 149,722.83 \times 0.006125 \approx 916.83$$Principal portion of the second payment:$$Principal\ portion = Total\ monthly\ payment - Interest = 1,194.67 - 916.83 \approx 277.84$$The closest answer to this calculation is $277.61, which is option B. The slight discrepancy in the final cent value is due to rounding during the calculation process.

Question 12

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 13

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

Total interest paid = $30,000 × 0.0475 × 5 = $7,125.00

Question 14

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 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 correct answer is A because 8.38 percent is the highest rate that can be afforded on a 48-month APR loan with monthly payments of $1,160.

Question 16

On this date last year,you borrowed $3,400.You have to repay the loan principal plus all of the interest six years from today.The payment that is required at that time is $6,000.What is the interest rate on this loan?

Accepted Answer

Using the formula for compound interest, we can solve for the interest rate:
$6,000 = $3,400 (1 + r)^6
Dividing both sides by $3,400:
1.7647 = (1 + r)^6
Taking the sixth root of both sides:
1 + r = 1.0845
Subtracting 1 from both sides:
r = 0.0845 or 8.45%

Therefore, the interest rate on this loan is 8.45%.

Question 17

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 monthly payment can be calculated using the formula for an amortizing loan. The interest portion of the first payment is $220,000 * (8.25% / 12), and the rest goes to the principal. The second payment's principal portion is slightly higher as the principal balance decreases.

Question 18

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 19

John's Auto Repair just took out a $52,000,10-year,8 percent,interest-only loan from the bank.Payments are made annually.What is the amount of the loan payment in year 10?

Accepted Answer

Payment in year 10 = $52,000 + ($52,000 × 0.08) = $56,160

Question 20

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

Quiz 6: Discounted Cash Flow Valuation