All fifteen questions and answers can be purchased at Teachers Pay Teachers at the link below.
Question One: A person is considering taking out a $180,000
mortgage and must choose between a 15year FRM and a 30year FRM. The interest rate on the 15year mortgage is
2.90 while the interest rate on the 30year mortgage is 3.40.
What are the monthly payments on the two loans?
What are the total interest payments on the two loans over
the life of the loan?
What is the aftertax cost of the interest payments on the
two loans?
What is the tax savings from the tax deductibility of
mortgage interest?
What is remaining loan balance after 15 years for the two
loans?
Question Two: Consider the 15year FRM and the 30year FRM
10 years after mortgage origination.
Both homeowners plan to stay in their home with their mortgage for an
additional 5 years.
What is the reduction in the mortgage balance over these
five years?
What are total interest payments for the two homeowners over
this fiveyear period?
Question Three examines the impact of a bad credit rating.
Question Three: Consider two people one with good credit and
one with bad credit. Each person has a
car loan, a 30year FRM, and a personal student loan. The date of origination of each loan, the
term of each loan, and the interest rate on each loan for the two people are
presented in the table below. What was
the interest paid on these loans for the two people in 2014?
Loan information for Two
People


Bad Credit Rate

Good Credit Rate

Term of Loan in Years

Loan Origination Date

Initial Loan Balance


Car Loan

0.11

0.04

6

1/1/13

$15,000

Personal Student Loan
Rate

0.12

0.06

20

1/1/10

$45,000

Mortgage Rate

0.055

0.0325

30

6/1/13

$320,000

Question Four: A person has $15,000 in credit card debt
divided over 5 credit cards with identical terms. The interest rate on all five cards is 12%. The minimum required monthly payment is 3.0%
of the monthly balance.
How long would it take for the person to repay the entire
$15,000 in credit card debt if the person continues to pay 3.0% of $15,000?
How long would it take for the person to cut the loan
balance in half if the person continues to make this monthly payment?
Question Five: Consider the person in problem four with five
credit cards each with a $3,000 balance, a 3% minimum payment requirement, and
a 12% interest rate. In addition, each
card has an annual fee of $60. The
credit card holder pays the annual fee with $5.00 monthly installments.
What is the person’s credit card balance after 41
months? How long would it take the
person to repay all credit cards when the $5.00 fee is included?
http://financememos.blogspot.com/2015/11/questionfivepayoffdebtforcredit.html
Question Six, Seven Eight, Nine, and Ten all deal with how student debt and credit card debt impact mortgage markets.
What monthly income does this person need in order to qualify
for a $300,000 mortgage if the mortgage interest rate on a 30year FRM is
4.25%?
How much income does the person need to qualify for the same
loan if the student loan is converted to a 20year term?
Modify the student debt and mortgage qualification spreadsheet
to calculate the amount of income needed to qualify for a $300,000 mortgage at
4.25% if the minimum required credit card payment is 3.0% of the monthly credit
card balance.
What is the required income for the mortgage if the student
loan is kept at a 10year term and if the student loan is moved to a 20year
term?
Question Eight: A person has a $80,000 student loan at a 7.0% interest
rate. The student debt is the person’s
only debt. The person can set the term
of the loan at 10 years or 20 years.
The person makes $95,000 per year.
The person is seeking a mortgage.
The mortgage payment must be less than 28% of monthly income. In addition, total monthly debt payments
must be less than or equal to 38% of monthly income. The current mortgage rate is 4.5%.
Create a spreadsheet
that calculates the amount of mortgage this person can qualify for if the
student loan is set at a 10year term and if the student loan is set at a
20year term.
How much mortgage can the person qualify for at current
interest rates?
How much mortgage could the person qualify for if the
student loan interest rate rose by 10%?
How much mortgage could the person qualify for if the
mortgage rate rose by 10%?
Question Nine: Consider the information on income and
student debt in the table below on five recent college graduates in the table
below. All student loans have a 10year
term and a 7.0% interest rate. The
interest rate on all mortgages is 5.0%.
Use the calculator on the maximum allowable mortgage to determine how
many of these five people will qualify for a $300,000 mortgage.
Income and Student Debt
Information for Five College Graduates


Income

Student Debt


1

$95,000

$80,000

2

$60,000

$20,000

3

$120,000

$67,000

4

$80,000

$110,000

5

$75,000

$30,000

The second person graduates college with a lot of student
debt and chooses to wait five years before buying an identical house. The second person also gets a 30year FRM
with an interest rate of 5.0% and a LTV of 90%.
The price of both houses increases 2.0% per year for a
15year period. What is the house equity
for the two people after 15 years?
http://financememos.blogspot.com/2015/11/questiontenimpactofhousepurchase.html
Questions Eleven and Twelve involve the calculation of house equity over a lifetime for people who might purchase more than one home. The strategic variable in question eleven is the type of mortgage. The strategic variable in question twelve is the number of times a person moves.
http://financememos.blogspot.com/2015/11/questiontenimpactofhousepurchase.html
Questions Eleven and Twelve involve the calculation of house equity over a lifetime for people who might purchase more than one home. The strategic variable in question eleven is the type of mortgage. The strategic variable in question twelve is the number of times a person moves.
All equity obtained after the sale of the first home and the
subtraction of a 6% sales commission is used as a down payment for the purchase
of the second home.
The real estate transactions for the two consumers differ in
two respects  (1) the term of the loans and (2) the interest rates on the
loan.
·
The first consumer uses 30year FRMs. The interest rate on the first house was
3.84% and the interest rate on the second house was 6.5%.
·
The second consumer uses 15year FRM. The interest rate on the first home is
0.0308. The interest rate on the second
house was 5.2%.
House prices increased 1.0% per year.
What is the available equity after the sale of the second
house for the two house buyers?
In this problem all houses are purchased with 15year FRM at
an interest rate of 5.0%. Also, all
houses appreciate in value at a rate of 1.0% per year.
At the beginning of a 15year period two people purchase a
$300,000 house. One person stays in the
same house for all 15 years. The other
person buys a new house identical in value to the he is currently living in
after 7 years.
The sales commission on the first house is 6.0%. In addition, closing costs on the new house
are equal to 4.0% of the house price.
The second person lives in his second house for eight more
years.
How much equity do the two people have after 15 years?
Question Thirteen involves the net present value of the tax deduction for mortgage interest for two types of mortgages.
Question Thirteen looks at the Net Present Value of different mortgages.
The interest rate on the 30year
FRM is 3.84%
The interest rate on the 15year
FRM is 4.5%.
The marginal tax rate is 30%.
Question Fourteen involves the impact of sequential market risk on 401(k) assets. It shows the timing of returns impacts final wealth.
Question Fourteen: Consider
a person age 50 with 15 years to go prior to retirement. The person has $200,000 in his 401(k)
plan. The person makes $80,000 a year
and invests 10% of her salary in ongoing biweekly contributions.
What is the final balance in the
401(k) plan if biweekly returns are 0.06/26 for the first 10 years and
0.07/26 for the last five years?
What is the final balance in the
401(k) plan if biweekly returns are 0.07/26 for the first five years and
0.06/26 for the next 10 years?
Observe the average return over
the two time periods is identical.
However, the sequence of returns differs.
Does the sequence of returns
impact the 401(k) balance? Why?
The final question consider whether it makes economic sense to buy a Toyota Prius instead of a Toyota Corolla.
Question Fifteen:
The table below contains information on the price and the fuel efficiency for a
Toyota Prius and a Toyota Corolla.
Fuel Efficiency for the
Prius and Corolla


Toyota
Prius

Toyota
Corolla


City

51

30

Highway

48

42

The cost of the Prius and the Corolla are presented below.
Cost of Prius and Corolla


Prius

Corolla


$24,200

16,800

Assume both cars are driven $15,000 per year with two thirds
of the driving in the city and 1/3 of the driving on the highway.
Gas is bought on a biweekly basis. The price of gas is $3.00 per gallon. Both cars are driven for 12 years.
The cost of capital for the car owners is 5.0%.
Under these circumstances does it make sense to choose the
Corolla or the Prius?
What gas price would result in the Prius being more
economical than the Corolla?
Change the assumptions on miles driven to 18,000 per year
for both drivers and the composition of driving to 90% city and 10%
highway. Assume the gasoline price goes
to and stays at $4.50 per gallon. How
do the costs of the Prius and the Corolla now compare?
Excel is a powerful tool. I hope these finance math problems help people learn how to use it.
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