Question 1

Your current $155,000 mortgage calls for monthly payments over 25 years at an annual rate interest rate of 6 percent.If you pay an additional $50 each month beginning with the first payment,how much interest expense do you save by pre-paying?

Accepted Answer

First, we need to calculate the original monthly mortgage payment. We can use the PMT function in Excel or a financial calculator to find this value. Using the information given, we get:

PMT = -$926.23

(We use a negative sign because this represents a payment.)

Next, we need to calculate the new monthly mortgage payment with the additional $50 payment. This can also be done using the PMT function. Since the payment is increasing, the present value (PV) of the loan will be decreasing with each payment. Therefore, we need to use the original loan amount minus the payments that have already been made as the present value. This gives us:

PMT = -$976.23

So the additional $50 payment increases the monthly payment by $50.

Now we can calculate the interest savings by pre-paying. We can do this by comparing the total interest paid for the original mortgage with the total interest paid for the mortgage with the $50 pre-payment. Again, we can use Excel or a financial calculator to do this.

For the original mortgage:

Total interest = -$155,000 x 6% x 25 years = -$139,500

For the new mortgage with the $50 payment:

Total interest = -$155,000 x 6% x 25 years - ($50 x 12 x 25) = -$122,347.78

(Note that we are subtracting the total additional payments made over the life of the loan.)

So the interest savings is:

Interest savings = -$139,500 - (-$122,347.78) = -$17,152.22

Therefore, the answer is:

Answer: C

Question 2

Loan Payments You wish to buy a $20,000 car.The dealer offers you a 3-year loan with an 8 percent APR.What are the monthly payments? How would the payment differ if you paid interest only? What would the consequences of such a decision be?

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The answer of Loan Payments You wish to buy a...

Question 3

Describe how compounding affects the future value computation of an annuity.

Accepted Answer

The answer of Describe how compounding affects the future value...

Question 4

Annuity Payments and Amortization Schedule Consider Carrie asks Miranda to help with her 20 percent down payment on her apartment.Miranda is willing to loan Carrie $30,000,but she is requiring 6.5 percent interest and semi-annual payments over three years to repay the loan.Carrie wants to deduct the loan's interest from her taxes,and Miranda must show the interest income on her taxes,so they need to know how much interest is included each year in the payments.Compute the semi-annual payments and create an amortization schedule to determine the interest paid each year.

Accepted Answer

The answer of Annuity Payments and Amortization Schedule Consider Carrie...

Question 5

Present Value of an Annuity Carrie and Miranda earn the same salary.However,Miranda has been far more financially responsible.She pays her bills on time and pays off her credit card debt quickly.Carrie had been less financially responsible.She often buys too many shoes and has allowed her credit card balance to balloon.If she is short on cash for a month,she simply decides to not even pay the minimum balance due on her credit card.Now they both are looking to buy apartments.Miranda decides she can afford to make $3,500 payments,but Carrie can only make $1,500 payments and pay off her credit card debt,too.Miranda qualifies for a 6 percent,30-year mortgage,but because of her bad credit rating Carrie will be charged 7.5 percent on a 30-year mortgage.Both will put 20 percent down.How is Carrie's bad credit going to impact her apartment search?

Accepted Answer

The answer of Present Value of an Annuity Carrie and...

Question 6

Your current $95,000 mortgage calls for monthly payments over 30 years at an annual rate interest rate of 6 percent.If you pay an additional $50 each month beginning with the first payment,how soon do you pay off your mortgage?

Accepted Answer

To solve this problem we will use the formula for the present value of an annuity:

PV = A * [(1 - (1 + r)^(-n)) / r]

Where:
PV = present value or the initial loan amount ($95,000)
A = monthly payment ($572.90)
r = monthly interest rate (6% / 12 = 0.005)
n = total number of payments (30 years * 12 = 360 months)

Using this formula, we can find the present value of the loan:

PV = 572.90 * [(1 - (1 + 0.005)^(-360)) / 0.005] = $95,000

Now, if we add $50 to the monthly payment, the new monthly payment will be $622.90. We want to find out how long it will take to pay off the loan with this higher payment amount. We can use the same formula:

PV = 622.90 * [(1 - (1 + 0.005)^(-n)) / 0.005]

We want to solve for n, so we'll need to use a numerical method like trial and error or a financial calculator. Using trial and error, we find that the answer is approximately 291.78 months, or about 24 years and 3 months. Therefore, the best choice is C.

Question 7

Explain why the effective annual rate (EAR)is a more accurate measure of the interest rate paid than the annual percentage rate (APR)?

Accepted Answer

The answer of Explain why the effective annual rate (EAR)is...

Question 8

What is the difference between an annuity due and an ordinary annuity?

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The answer of What is the difference between an annuity...

Question 9

Future Value and Annuity Payments Chandler and Monica are trying to decide if they will have enough money to retire early in 15 years,at age 60.Their current assets are $250,000 in retirement plans and they have $80,000 in other investments.Together,they contribute $30,000 per year to their retirement plans and another $6,000 to other investments.If their assets grow at 9 percent per year,how much money will they have when they turn 60? After they retire,they will invest their wealth more conservatively and it will earn 6 percent per year.Is this enough to fund a $150,000 per year retirement for 30 years?

Accepted Answer

The answer of Future Value and Annuity Payments Chandler and...

Question 10

After saving diligently your entire career,you and your spouse are ready to retire with a nest egg of $500,000.You need to invest this money in a mix of stocks and bonds that will allow you to earn $4,000 per month for 30 years.What annual interest rate (APR)do you need to earn?

Accepted Answer

To find the required annual interest rate to earn $4,000 per month for 30 years from a $500,000 investment, we can use the formula for the present value of an annuity. The monthly withdrawal of $4,000 translates to $48,000 annually. Using financial calculators or present value of annuity formulas, we find that an annual interest rate of approximately 8.94% is needed to sustain these withdrawals for 30 years from a $500,000 nest egg.

Question 11

Compound Frequency Say that you own a small business,which you plan to expand.Your expansion plans include borrowing $100,000 from the bank with a five-year,amortized loan.The bank has given you three loan choices:
Annual payments at 8.85 percent APR
Quarterly payments at 8.75 percent APR
Monthly payments at 8.65 percent APR

Accepted Answer

The answer of Compound Frequency Say that you own a...

Question 12

Your current $115,000 mortgage calls for monthly payments over 30 years at an annual rate interest rate of 7 percent.If you pay an additional $50 each month beginning with the first payment,how much interest expense do you save by pre-paying?

Accepted Answer

The answer of Your current $115,000 mortgage calls for monthly...

Question 13

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

Accepted Answer

The present value of an annuity increases when the interest rate decreases because the discount factor used in calculating present value is inversely related to the interest rate. Lower interest rates result in higher present values for future cash flows.

Question 14

Loan Payments You wish to buy a $30,000 car.The dealer offers you a 4-year loan with a 6 percent APR.What are the monthly payments? How would the payment differ if you paid interest only? What would the consequences of such a decision be?

Accepted Answer

The answer of Loan Payments You wish to buy a...

Question 15

How might credit card companies keep their cardholders in debt for a long time?

Accepted Answer

The answer of How might credit card companies keep their...

Question 16

The interest on your home mortgage is tax deductible.Why are the early years of the mortgage more helpful in reducing taxes than the later years?

Accepted Answer

The answer of The interest on your home mortgage is...

Question 17

Present Value of an Annuity Carrie and Miranda earn the same salary.However,Miranda has been far more financially responsible.She pays her bills on time and pays off her credit card debt quickly.Carrie had been less financially responsible.She often buys too many shoes and has allowed her credit card balance to balloon.If she is short on cash for a month,she simply decides to not even pay the minimum balance due on her credit card.Now they both are looking to buy apartments.Miranda decides she can afford to make $2,500 payments,but Carrie can only make $2,000 payments and pay off her credit card debt,too.Miranda qualifies for a 6.5 percent,30-year mortgage,but because of her bad credit rating Carrie will be charged 8 percent on a 30-year mortgage.Both will put 20 percent down.How is Carrie's bad credit going to impact her apartment search?

Accepted Answer

The answer of Present Value of an Annuity Carrie and...

Question 18

After saving diligently your entire career,you and your spouse are ready to retire with a nest egg of $600,000.You need to invest this money in a mix of stocks and bonds that will allow you to earn $5,000 per month for 30 years.What annual interest rate (APR)do you need to earn?

Accepted Answer

The answer of After saving diligently your entire career,you and...

Question 19

Which of the following will increase the future value of an annuity?

Accepted Answer

All three factors will increase the future value of an annuity. Increasing the number of periods or the amount of the annuity will increase the total amount of money invested over time, which will result in a higher future value. Additionally, a higher interest rate will result in greater returns on the investment, which will also increase the future value.

Quiz 5: Time Value of Money