Expert: Scott A Wilson - 12/19/2008

Question
Hey, my question is extremely long, and I hope you don't mind helping me out with it, because I'm definately stuck.

You are a teacher and make $55,000 after taxes. This means you take home $49,000 a year. You have also inherited $25,000 and will use that for the downpayment, laywers fees and land transfer taxes.

1. You housing costs should not exceed 32% of your monthly take home income.
2. the interest rate that is set out by the bank is 5% which is also called PRIME.
3. the bank you've decided to go with has given you an interest rate of prime minus 0.5% which is the variable rate. As prime fluctuates, your interest rate will always be 0.5% below prime. This rate is attached to a 5 year plan.
4. the company that lends the money for mortgages charges an insurance premium of 3%. the insurance premium is calclated by taking the selling price of the home, subtracting the downpayment, multiplying by 3% and adding the answer to the selling price subtract the downpayment.
5. the bank has 4 ammortizations to choose from 25,30,35 and 40 years.

EXAMPLE:

Step 1: Selling Price = 164,900
       Downpayment = $10,000    
Selling price - Downpayment = Mortgage before insurance
       164,900 - 10,000 = 154,900
Step 2: Mortgage before insurance x Insurance rate = insurance premium
       154,900 x 0.03 = 4647
Step 3: Mortgage before insurance + insurance premium = final mortgage amount
       154,900 + 4647 = 159547 <- this value is the PV value used in calculations.

To help on closing the deal you hire a lawyer. The  percentage you pay to the lawyer is 1.83% of the selling price, subtract the downpayment.

The property taxes are based on the selling price of the house (the sticker price of the house if you will.) This value must be taken into consideration for your 32% monthly housing cost.

Propety tax = 1.1%

After two years at thid rate, prime has gone up to 6.2%. Which means now you have to calculate your new monthly payment for the remainder of your 5 year term.

After another 2 years prime has gone up again to 7.1% Fearing prime willl go up you call your banker and ask for available options. You decide to lock in to another 5 year term at 6.7%, with your previous deal of 0.5% below prime no longer offered. What are your monthly payments for the next 5 years?


This is how far I got.

164,900 asking price of house.

Monthly income:
49,000 / 12 = 4083.33

32% of monthly income :
4083.33 x .32 = 1306.67

10,000 downpayment.

Lawyers fees:
164,900 - 10,000 x .0183 = 2834.67

Insurance fee:
164,900 - 10,000 x .03 = 4647.00

Land tax:

164,900 x .011 = 1813.90
1813.90 / 12 = 151.16 per month  

Answer
Income: 55K; take home: 49K
Inherited: 25K, use for lawyer, closing, etc.

1. Take 49K*0.32 to get $15,680.

2. Interest rate is 5% = 0.05, called PRIME.

3. Bank interest rate is 0.045, but fluctuates with the PRIME, yet is always ≤5%.  This is attached to a 5 year plan.

4. Premium of 3% of (selling price - down payment)

5. Bank will let you choose between 25,30,35 and 40 years.
Which one was selected?

EXAMPLE:

Step 1: total price: %164,900, down payment: $10,000    
Selling price: 164,900 - 10,000 = 154,900

Step 2: mg 154,900 x 0.03 = 4647

Step 3: $154,900 + $4,647 = $159,547 <- PV

Lawyer: 1.83% of the selling price (price – down payment)

Property tax: 32% of total price

Property tax = 1.1%

Note on step 3, the bank agreed that the lending rate would be ≤5% for the first 5 years.


What is 'after two yeard at thid rate ...' thid??  Is that suppose to be ‘after two years at this rate …’

For how many years was the mortgage planned?

Does the 'remainder of your 5 year term' mean that you planned to do it in 5 years?  Ignoring that, let's keep looking at the problem.


After another 2 years prime has gone up again to 7.1% Fearing prime will go up you call your banker and ask for available options. You decide to lock in to another 5 year term at 6.7%, with your previous deal of 0.5% below prime no longer offered. What are your monthly payments for the next 5 years?


This is how far I got.

164,900 asking price of house.

Monthly income:
49,000 / 12 = 4083.33

32% of monthly income:
4083.33 x .32 = 1306.67

10,000 down payment.

Lawyers fees:
164,900 - 10,000 x .0183 = 2834.67 (paid only once)

Insurance fee:
164,900 - 10,000 x .03 = 4647.00 (paid every year)
This would be 4647/12= 387.25 (per month)

Land tax:

164,900 x .011 = 1813.90 (paid every year)
1813.90 / 12 = 151.16 (per month)



It would look like you have an initial fee of $10,000 + $3,824.67 = $13,824,67.

The basic fee per month would be $387.25 + $151.16 = $538.41.  We'll add the price of the house to that in a moment.

To calculate the future value, F, given the annuity payment, A, the equation would be A = i*F / ((1+i)^N-1) and to calculate F,
F = (1+i)^N * P.  Here, N is the number of months and i is the monthly insurance.  Note that the monthly fee ($538.41) would also have to be added to A to get the total amount owed per month.

At each of the points, you could take the amount left and compute the monthly payment given the interest rate and in how many years it will be done.  Note again that the yearly interest rate needs to be divided by 12 and the amount of years needs to be multiplied by 12 since we are talking about months.