Question

Kathy wants to buy a condominium selling for ​$97,000. The taxes on the property are ​$1500 per​ year, and​ homeowners' insurance is ​$336 per year. Kathy's gross monthly income is ​$5000. She has 15 monthly payments of ​$145 remaining on her van. The bank is requiring​ 20% down and is charging a​ 9.5% interest rate with no points. Her bank will approve a loan that has a total monthly mortgage payment of​ principal, interest, property​ taxes, and​ homeowners' insurance that is less than or equal to​ 28% of her adjusted monthly income. Complete parts ​a) through h​) below.

a) Determine the required down payment.

The required down payment is

​b) Determine 28​% of her adjusted monthly income.

28​% of her adjusted monthly income is

​c) Determine the monthly payments of principal and interest for a​ 25-year loan.

The monthly payment of principal and interest for a​ 25-year loan is

​d) Determine her monthly​ payment, including​ homeowners' insurance and taxes.

Her total monthly​ payment, including​ homeowners' insurance and taxes is

​e) Does Kathy qualify for the​ loan?

​f) Determine how much of the first payment on the loan is applied to the principal.

The amount of the first payment that is applied to the principal is

g) Determine the total amount she pays for the condominium with a​ 25-year conventional loan.​ (Do not include taxes or​ homeowners' insurance.)

The total amount paid is

​h) Determine the total interest paid for the​ 25-year loan.

The total interest paid is ​

Answer 1

A) Down payment calculation is quite simple. In this particular case, the bank has asked for a 20% down payment which essentially is 20% of the cost of the condominium.

Cost of Condominium= $97000

Down Payment = 97000*20% = $19400

B) Adjusted monthly income is basically gross monthly income less any obligations to be paid. in the case above- Kathy has an obligation to pay $145 per month towards a car loan

Thus her adjusted is as follows

Gross monthly income= $5000

Interest payment towards car loan= $145

Adjusted monthly income= 5000-145 = $4855

Thus 28% of her adjusted monthly income is

4855*28% = $1359

C) for calculating monthly principle and interest payments we first need to calculate the following

Principle (P)= $97000 - $19400 = $77600 (less down payment)

Annual interest rate (i) = 9.5%

Thus monthly = 9.5/12 = 0.79%

Length of loan (n) = 25 years *12 = 300 months

Monthly principle and interest payments =P* i /(1-(1/(1+i)^n))

=77600 * 0.79%/(1-(1/(1+0.79%)^300))

=$676.91

D) Now we need to determine her monthly payment including property taxes and homeowners insurance

all we need to do is calculate the tax and insurance at a monthly rate and add it to out monthly mortgage payment

for property taxes = 1500/12 = $125 pm

for homeowners insurance = 336/12 = $28 pm

Thus total payment = $676.91 + $125 + $28 = $829.91

E) Yes Kathy does qualify for the loan since the total monthly payment is less than 28% of her monthly adjusted income

F) The monthly mortage payment less the interest element will be the amount that applies to the principal from the first payment. thus

676.91(1-0.79%)= $671.56

G) The total amount payable for a 25year loan will be

$676.91 *300 = $203073