Question

[The information presented here applies to questions 1 & 2] You borrowed the $265,000 needed to acquire your new condo in Jersey City with a 3/1 ARM. The rate on the loan is determined by the yield on a Cost of Funds Index (COFI) plus a margin of 325 basis points (3.25%). If the COFI index was at 1% at the time you received the loan, what was your scheduled monthly payment for the first three years? At the first reset date, the COFI is 1.25%, what is your scheduled monthly payment for the fourth year of your loan?

Answer 1

To calculate EMI = [P x R x (1+R)^N]/[(1+R)^N-1], where P stands for the loan amount or principal, R is the interest rate per month and and N is the number of monthly instalments.

A 3 Year ARM (3/1 ARM) is a loan with a fixed rate for the first three years that has a rate that changes once each year for the remaining life of the loan. Because the interest rate can change after the first three years.

We will calculate the monthly EMI from the formula mentioned above.

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

P= principal ($265,000)

Rate= 4.25% (for first three year) 4.5% from fourth year.

N = 10 Years (10 years is assumed, since period is not mentioned, however in the formula just change no. of year)

Part-1 Calculation of the monthly EMI for first 3 years.

($265,000* 4.25%/12 (1+4.25%)^120)/((1+4.25%/12)^120-1)

Monthly EMI 2,714

The R is divided by 12 as we have to calculate monthly payment same why the N is multiplied by no. of Months

Part-2 Calculation of the monthly EMI from 4^th Year.

We have already paid monthly installment of 2714 per month. Total principal remaining is 196,920.

We will use the same formula used for calculating EMI

($196,920* 4.5%/12 (1+4.5%)^84)/((1+4.5%/12)^84-1)

Monthly EMI 2,737