Question

What is the loan balance after 5 years on a conventional fixed-rate 6.5% mortgage with the original maturity of 30 years and initial balance of $100,000? Assume only required monthly payments have been made.

• A. $99,543
• B. $93,735
• C. $93,611
• D. $83,581
• E. $83,333
  

Answer 1

Given about a conventional fixed rate mortgage loan,

Interest rate r = 6.5%

Years of loan t = 30

Initial balance PV = $100000

So, Monthly payment on the loan,

PMT = PV*(r/n)/(1 - (1+r/n)^(-n*t)) = 100000*(0.065/12)/(1 - (1+0.065/12)^(-12*30)) = $632.07

After 5 years, loan period remaining is 25 years

So, loan balance after 5 years is present value of monthly payments remaining:

So, loan balance PV = PMT*(1 - (1+r)^(-t*n))/(r/n) = 632.07*(1 - (1+0.065/12)^(-12*25))/(0.065/12) = $93611

So, Option C is correct.