Question

Kathy wants to buy a condominium selling for ​$96,000. The taxes on the property are ​$1400 per​ year, and​ homeowners' insurance is ​$346 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

​$

​(Round to the nearest cent as​ needed.)

​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

​$

​(Round to the nearest cent as​ needed.)

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

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

​$

​(Round to the nearest cent as​ needed.)

​e) Does Kathy qualify for the​ loan?

Yes

No

​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

​$

​(Round to the nearest cent as​ needed.)

​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

​$.

​(Round to the nearest dollar as​ needed.)

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

The total interest paid is $

​ (Round to the nearest dollar as​ needed.)

Answer 1

a. Required down payment

96000*20%=

19200

b. 28% of adjusted monthly income is:

(5000-145)*28%=

1359.4

​c. Monthly payments of principal and interest for a​ 25-year loan.

Using PV of ordinary annuity formula,

with PV of the bank loan =96000*80%=76800

No.of periods=25*12=300

at monthly interest of 9.5%/12=

76800=Pmt.*(1-1.00792^-300)/0.00792

Solving the above, we get the monthly payment as

671

d.Total monthly payment=

671+((346+1400)/12)=

817

e.YES---- 817 < 1359.4

​f)Amt.of First payment on the loan applied to the principal:

671-(76800*0.00792)=

62.74

ie.$ 63

​g.Total amount she pays for the condominium with a​ 25-year conventional loan(without including taxes &​ homeowners' insurance)

671*12 mths. *25 yrs. =

201300

​h) So, Total interest paid for the​ 25-year loan:

201300-76800=

124500