Question

You have been living in the house you bought 7 years ago for $300,000. At that time, you took out a loan for 80% of the house at a fixed rate 15-year loan at an annual stated rate of 7.5%. You have just paid off the 84th monthly payment. Interest rates have meanwhile dropped steadily to 5.0% per year, and you think it is finally time to refinance the remaining balance over the residual loan life. But there is a catch. The fee to refinance your loan is $5,000. Should you refinance the remaining balance? How much would you save/lose if you decided to refinance?

Answer 1

Given that ,

The cost of House = $300000

Out of which , 80 % is loan = 300000*80%= 240000

Time period- 15 years

Anual rate of Interest during Loan = 7.5%

we have paid 84th monthly installment, which is nothing but of the 15 years term , we have repaid for around 7 years.

Assuming that for te 7 years (84 months we have paid interest at te rate of 7.5% Per annum.

As stated in the question , the Interest rate has now fallen to 5% Annually

First let us calculate the total amount to be paid ,

Principal= 240000

Term= 15 years

Interest for first 7 years- 7.5%

From 7-15 years= 5% interest

So, the total amount (principal +Interest ) to be paid at 7.5 %will be =(240000/15)+(240000*7.5%)=34000 per year

For next 8 years considering 5% as interest = (240000/15)+(240000*5%)= 28000 per year

So the total amount = (34000*7)+(28000*8)= 462000

The amount we have already paid in 84 months (7years )=238000

Amount yet to be paid at 5 % Interest = 224000.

Refinancing the Loan: Refinancing of a loan is nothing but getting anoter loan to repay the current loan .This option may be choosed if the loan is available at cheap rate of interest than the original loan.

That is, taking new loan to settle the old loan is refinancing.

Given that the Fee to refinance is $5000 .

So, if the loan is settled immediately, the interest of further 8 years can be saved in the old loan.

That is after 8 years (at he end of 15th year ) he need to pay the remaining 224000.

But if he opt for refinancing, he needs to pay only the remaining amount excluding the interest of 8 years.

To calculate that,

original Principal= 240000

Principal paid at the end of 84th Installment= (24000/15)7= 112000

Remaining principal to be paid = 240000-112000= 128000.

If he opt for refinancing and settle the debt currently= 128000+5000(fees)

Amount he need to pay now= 133000.

If he refinance now, he can save around (224000-133000)=91000.

He can opt for Refinancing option as he could save around $91000.