Question

Susan Summers wants to buy a house for $320,000 in 5 years. She wants to put

20% down and apply for 30-year fixed mortgage to finance the rest. Mortgage

interest rate is 4%, annual property tax is 0. 9% of house value and homeowners

insurance is $100 per month. Assume expected rate of return on her savings is

2%. Expected inflation rate is 3%.

1. Calculate monthly mortgage payment.

2. Calculate housing expenses (front-end) ratio.

3. Calculate total debt-to-income (back-end) ratio.

4. Based on your calculation, can she afford the $320,000 house?

5. Calculate how much she needs to set aside every month to save enough

for down payment in 5 years.

6. Calculate how long it takes to save enough for down payments if she

saves $200 each month?

Answer 1

The loan amount will be 80% of $320,000, which is $256,000.

1. The monthly mortgage payment can be calculated using excel by using formula given below

monthly rate = .04/12 = 0.00333

Tenor = 30*12 = 360 months

= PMT(0.00333,360,256000,0)

=$1222.18

2) Housing expense ratio is the ratio of total expense are expected in every month which includes the principal and interest, property tax, and insurances.

So total expenses = 1222.18 (Principal plus interest) + 320000*.009/12 (property tax) + $100

                                = 1222.18+ 240 + 100

                                = 1562.18

Total income can be arrived by back calculating that she is saving 20% of loan amount in 5 years, hence every month income / savings would be $ 1066.67

Hence front end ratio is = 1562.18/1066.67

                                       = 1.46

3) Back end ratio is = 1562.18/1066.67

                                  = 1.46

4) According to me it is tough for her because her savings are getting decreased due to the inflation rate is higher than savings rate. So whatever savings she will have, the property prices will increase faster than her savings.