Question

A borrower takes out a 30-year adjustable rate mortgage loan for $325,000 with monthly payments. The first two years of the loan have a "teaser" rate of 4%, after that, the rate can reset with a 5% annual payment cap. On the reset date, the composite rate is 6%. Assume that the loan allows for negative amortization. What would be the outstanding balance on the loan at the end of Year 3?

Answer 1

Principal at year 0 (P) = $325,000

Interest rate (r)= 4%, Monthly = 4%/12 = 0.3333%

Period (n) = 30 years, Monthly = 30 * 12 = 360

PMT = P * r * (1 + r)^n / (1 + r)^n - 1

PMT = 325,000 * 0.3333% * (1 + 0.3333%)^360 / (1 + 0.3333%)^360 - 1

PMT = 325,000 * 0.003333 * (1.003333)^360 / (1.003333)^360 - 1

PMT = 325,000 * 0.003333 * 1.4323 = $1551.525

Outstanding Principal balance at year 2 = P * (1 + r)^n - PMT x (1 + r)^n -1 / r

Outstanding Principal balance at year 2 = 325,000 * (1 + 0.3333%)^24 - 1551.525 x (1 + 0.3333%)^24 -1 / 0.3333%

Outstanding Principal balance at year 2 = 325,000 * (1.003333)^24 - 1551.525 x (1.003333)^24 -1 / 0.003333

Outstanding Principal balance at year 2 = (325,000 * 1.0831) - 38,699.36

Outstanding Principal balance at year 2 = 352,018.70 - 38,699.36 = $313,319.30

Outstanding Principal (P) = $313,319.30

Interest rate at beginning of year 3 (r) = (Previous rate + 7%, Composite rate)

Interest rate at beginning of year 3 (r) = (4% + 5%,6%) = 6%, Monthly = 6%/12 = 0.5%

Outstanding payments (n) = 28 x 2 = 336

PMT = P * r * (1 + r)^n / (1 + r)^n - 1

PMT = 313,319.30 * 0.5% * (1 + 0.5%)^336 / (1 + 0.5%)^336 - 1

PMT = 313,319.30 * 0.005 * (1 .005)^336 / (1.005)^336 - 1

PMT = 313,319.30 * 0.005 * 1.2302 = $1927.302

Outstanding Principal balance at end of year 3 = P * (1 + r)^n - PMT x (1 + r)^n -1 / r

Outstanding Principal balance at end of year 3 = 313,319.30 * (1 + 0.5%)^12 - 1927.302 x (1 + 0.5)^12 -1 / 0.5

Outstanding Principal balance at end of year 3 = 313,319.30 * (1.005)^12 - 1927.302 x (1.005)^12 -1 / 0.005

Outstanding Principal balance at end of year 3 = (313,319.30 * 1.0617) - 23,774.35

Outstanding Principal balance at end of year 3 = 332,644.14 - 23,774.35 = $308,869.79

Therefore outstanding balance on the loan at the end of Year 3 will be $308,869.79 approx.