Question

For this project you need to come up with five what-ifs. You should use your own house if you have one. For instance you buy a $500,000 house, put 25% down and finance the rest at 5.5% for 30 years. Now suppose that after 15 years you decide to refinance at 4.7% for 30 years. How much would you save? Now jump to the bottom line and figure how much you save. Is there any ah hah moments? What if you increased the payment with an extra $250 each month? How much sooner would it take to pay off the house? If instead of refinancing at 15 years you decide to refinance at 10 years. How does the amount saved differ from the original problem? If you plan on buying this house and paying for it. How big is your budget for buying a house. According to the information given above.

Answer 1

Cost	500000
Down payment(25%*500000)	125000
Financed portion(500000-125000)	375000

1...Using PV of annuity formula,

monthly payment(EMI)-for 30yrs.*12-360 periods, on the above amt. financed at 5.5%/12 will be

375000=Pmt.*(1-1.004583^-360)/0.004583

Solving for the monthly payment ,we get

2129.11

So, total payment (principal +interest) will be

2129.11*12*30=

766480

Balance 180 payments pending under this arrangement=2129.11*180= 383240

2..Now suppose that after 15 years you decide to refinance at 4.7% for 30 years

We can find the Principal balance after 15*12=180 payments as follows:

FV of Original Loan Balance- FV of annuity

(375000*1.004583^180)-(2129.11*(1.004583^180-1)/0.004583)

260583

This principal ,will be refinanced at 4.7%/12 monthly for the next 30 yrs.

Now, the monthly payments will be

260583=Pmt.*(1-1.003917^-360)/0.003917

Solving for the monthly payment ,we get

1351.54

So, total payment (principal +interest) will be

1351.54*12*30=

486554

So,

Payments pending under the old(5.5%) arrangement= 383240

Same under under the new(4.7%)arrangement= 486554

So,additional amt. on the new option=486554-383240=

103314

No Savings

(due to extension of payment -period , by another 15 yrs.)

3.. If the payment is increased with an extra $250 each month?

Assuming the 1st option, again,

375000=(2129+250)*(1-1.004583^-n)/0.004583

Solving the above, we get,

n=280 months

How much sooner would it take to pay off the house?

360-280= 80 months, ie. Roughly 6.67 years sooner.

4..If instead of refinancing at 15 years you decide to refinance at 10 years. How does the amount saved differ from the original problem?

Now suppose that after 10 years you decide to refinance at 4.7% for 30 years

We can find the Principal balance after 10*12=120 payments as follows:

FV of Original Loan Balance- FV of annuity

(375000*1.004583^120)-(2129.11*(1.004583^120-1)/0.004583)=

309526

This principal ,will be refinanced at 4.7%/12 monthly for the next 30 yrs.

Now, the monthly payments will be

309526=Pmt.*(1-1.003917^-360)/0.003917

Solving for the monthly payment ,we get

1605.39

So, total payment (principal +interest) will be

1605.39*12*30=

577940

So,

Payments pending under the old(5.5%) arrangement=(2129.11*240)= 510986

Same under under the new(4.7%)arrangement= 577940

So,additional amt. on the new option=577940-510986=

66954

No Savings

(due to extension of payment -period , by another 15 yrs.)

The option of refinancing at the end of 10 yrs. ,ie. After 120 payments is less costlier than that at end of 15 yrs,ie.after 180 payments.

But the best option is full down payment   or

the 1st option of 25% down payment with 5.5% interest for 30 yrs.