Question

A house cost 79,000 with 6,900 down payment. If the mortgage rate was 15% instead of 14.5% for 30 years, what is the difference in the monthly payment?

Answer 1

Interest rate per month (15%) = 15/12 = 1.25% per month

Interest rate per month (14.5%) = 14.5/12 = 1.2083% per month

Loan term = 30*12 = 360 month

Loan amount = 79000 – 6900 = 72100

EMI @ 15%

If the loan amount is P, rate on interest (monthly is r, and loan term is n the EMI will be

EMI = P*r[(1 +r)^n]/ [(1+ r)^n- 1]

Where,

              Loan amount (P) = $72100

                Time (n) = 360

               Interest rate [r] = 1.25% /period

Let's put all the values in the formula to calculate EMI

EMI = 72100*0.0125[(1 +0.0125)^360]/ [(1+ 0.0125)^360- 1]

        = 901.25[(1.0125)^360]/ [(1.0125)^360- 1]

        = 901.25[87.5409951357]/ [87.5409951357- 1]

        = 901.25[87.5409951357]/ [86.5409951357]

        = 901.25[1.01155521725203]

        = 911.66

So EMI will be $911.66

EMI @ 14.5%

EMI = P*r[(1 +r)^n]/ [(1+ r)^n- 1]

Where,

              Loan amount (P) = $72100

                Time (n) = 360

               Interest rate [r] = 1.2083% /period

Let's put all the values in the formula to calculate EMI

EMI = 72100*0.012083[(1 +0.012083)^360]/ [(1+ 0.012083)^360- 1]

        = 871.1843[(1.012083)^360]/ [(1.012083)^360- 1]

        = 871.1843[75.4756428146]/ [75.4756428146- 1]

        = 871.1843[75.4756428146]/ [74.4756428146]

        = 871.1843[1.01342720871157]

        = 882.88

So EMI will be $882.88

Difference = 911.66 – 882.88 = 28.78