Question

Assume you have a 6% 30-year mortgage for $100,000 with now 10 years to maturity (annual payments with exactly one year to the next payment). You are considering a refinance of the loan at 4% with a refinancing fee of $4,000.

What is the remaining loan balance?

Answer 1

A 30 year mortgage

Where, Interest Rate = 6%

Time Period = 30 Years

Total Amount = $100,000

Amount paid per year =  [P x R x (1+R)^N]/[(1+R)^N-1]

[100000 * 6 * (1 + 6%)^30] /[(1 + 6%)^30 - 1] = 7264.89

This amount contains both principal and interest.

Remaining balance after 20 such payment = $ 53, 470.23

Use the formula : FV = PV(1 +r)^n - P[{(1+r)^n - 1}/r]

Where PV = 100,000

r = 6%

n = 20

p = 7264.89

FV = 53,470.23

Now in addition to this, 4000 remaining fees will be added. Therefore = The remaining loan balance amount = 57,470.23