Question

A while ago, a couple purchased a home with a sales price of $790,000, making a 10% down payment and financing the rest with a 30-year adjustable rate mortgage fixed at 3.6% for the first six years. Now that the fixed rate period is up, the couple is facing a higher adjustable rate. They now plan to refinance into a fixed rate 15-year mortgage at 4.6%, allowing them to pay it off before they retire. What will their new monthly payments be? Assume there are no costs associated with the refinance.

Answer 1

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

Where, P = Loan Amount, R= Rate, N = No of Installments

So, EMI for First 6 Years will be = [ (790000*90%) * (3.6/100*12) * (1+(3.6/100*12))^(30*12)) ] / [ (1+(3.6/100*12)^(30*12) - 1]

So, EMI = 3233.

Amortisation for first 6 years =>

Now we calculate the Prinicpal component in the EMI for the 6th year final Installment ie for 6*12 = 72nd month. The formula is

{1 / (1+ R)}^(N- M+1) X EMI. (M is the paid EMI)

ie, { 1 / (1+ (3.6/100/12) } ^ (30*12 - 72 +1) * 3233 = 1360.30

So Interest = (3233 - 1360.3) = 1872.7

Now Interest per month = 3.6/12 = 0.3.

So principal outstanding at beginning of 72nd month = 1872/0.3 *100 = 624233.3

We subtract the principal component of 72nd month, we get the outstanding loan for remaining years ie 624233.3 - 1360.3 = 622873.00.

So EMI for remaining tenure => EMI = [P x R x (1+R)^N]/[(1+R)^N-1]

ie, = [622873* (4.6/100/12) * (1+ (4.6/100/12)^(15*12)] / [(1+ (4.6/100/12))^(15*12)-1]

= 4976.83

So, new monthly payments = 4976.83.

Please comment in case of any query