Question

On June 1, you borrowed $230,000 to buy a house. The mortgage rate is 8 percent. The loan is to be repaid in equal monthly payments over 20 years. The first payment is due on July 1. Assume that each month is equal to 1/12 of a year. How much of the second payment (on August 1) applies to the principal balance? $ How much of the second payment (on August 1) is interest? $ How much of the third payment (on September 1) applies to the principal balance? $

Answer 1

Formula for monthly payments (EMI) –

P = EMI/ (1+r) + EMI/ (1+r)² +………….+ EMI / (1+r)^N

=>   EMI = [P * r * (1+r)^N ] / [(1+r)^N – 1]

where,

P = Loan Borrowed = Principal = $230,000

r = monthly rate = 8%/12 = 0.6667%

N = No of months = 20 * 12 = 240

So, EMI = [230,000 * 0.0067 * (1+0.006667)²⁴⁰ ] / [(1+0.006667)²⁴⁰ – 1]

=> EMI = $1923.87 = $1924

Table for payments for first four months is as follows -

Month	Opening Principal	EMI	Interest (Opening Principal * 8%/12)	Principal Repayment (EMI _ Interest)	Closing Principal (Opening Principal – Principal Repayment)
1 (July 1)	230,000	1,924	1,533	390	229,610
2 (Aug 1)	229,610	1,924	1,531	393	229,216
3 (Sep 1)	229,216	1,924	1,528	396	228,821
4 (Oct 1)	228,821	1,924	1,525	398	228,422

For second payment on 1^st Aug, $1,531 payment is for interest and $390 is for principal repayment.

For third payment on 1^st Sep, $1,528 payment is for interest and $393 is for principal repayment