Ten years ago, you wisely beught a Newark house near NJIT for $120,000. The clos

Question

Ten years ago, you wisely beught a Newark house near NJIT for $120,000. The closing costs were an additional $5,000. You paid the closing costs plus put $20,000 down, and you obtained a 9% (compounded monthly) $100,000 mortgage for 30 years for the remainder. a) What is your monthly mortgage payment (just "Principal and Interest," that is, ignoring taxes, insurance, etc.)? b) Today, exactly 10 years later with 20 years of payments remaining, mortgage interest rates have dropped to 6%, still compounded monthly. If you were to refinance the remaining balance of your loan at the new 6% rate for the remaining 20 years, how much lower would your monthly payments be?

Explanation / Answer

a)

Calculation of monthly mortgage payment:

EMI = [P x R x (1+R)^N]/[(1+R)^N-1]

= $100,000 * 0.0075* (1+0.0075)^360 / (1+0.0075)^360-1

= $804.62 per month

where

P stands for the loan amount or principal = $100,000,

R is the interest rate per month = 9/12 = 0.75%

N = number of periods = 30 years * 12 months = 360 months

b)

EMI = [P x R x (1+R)^N]/[(1+R)^N-1]

= $89,430 * 0.0050* (1+0.0050)^240 / (1+0.0050)^240-1

= $640.7 per month

Monthly EMI would be lowered by  $163.92 ($804.62-$640.7).

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