Question

2. (25 Points) Suppose a borrower takes out a 30-year adjustable rate mortgage loan for $200,000 with monthly payments. The first two years of the loan have a "teaser" rate of 4%, after that, the rate can reset with a 2% annual rate cap. On the reset date, the composite rate is 7%. What would the Year 3 monthly payment be? (15 points) Step I Step2 PV= -179084.11 PV = -200 000 I= 7412=10.58) I=47212= 10.33) N= 336 N=360 130x2) (24) FV=0 Om T- FV=?$179,084Wis PMT= 1,212.36 3rd year monthly PMt) Dl what this

Answer 1

2. Principal loan outstanding at year 0 = $200,000
interest rate = 4%
No of payments outstainding = 30*12 = 360
Monthly payment = Principal outstanding * rate per month * [((1 + rate per month) ^ number of payment)/(((1 + rate per month) ^ number of payment) - 1)
= $200,000 *0.04/12 * [(1 + 0.04/12)^360/((1 + 0.04/12)^360 -1) = $955
Principal outstanding at end of year 2 = Principal outstanding ( 1 + rate per month) ^ no of payments made - monthly payment * [(1+ rate per month)^no of payment made - 1]/rate per month
= $200,000 * ( 1+0.04/12)^24 - $955 * [ (1+0.04)^24 - 1]/(0.04/12)
= $192,812

interest rate at beginning at year 3 = min(previous rate + 2%, composite rate) = min (4+2%,7%) = 6%
No of payments outstanding = 28*12 = 336
Monthly payment = Principal outstanding * rate per month * [((1 + rate per month) ^ number of payment)/(((1 + rate per month) ^ number of payment) - 1)
= $192,812 *0.06/12 * [(1 + 0.06/12)^336/((1 + 0.06/12)^336 -1) = $1,186

Principal loan outstanding at year 0 = $200,000
interest rate = 4%
No of payments outstainding = 30*12 = 360
Monthly payment = Principal outstanding * rate per month * [((1 + rate per month) ^ number of payment)/(((1 + rate per month) ^ number of payment) - 1)
= $200,000 *0.04/12 * [(1 + 0.04/12)^360/((1 + 0.04/12)^360 -1) = $955
Principal outstanding at end of year 2 = Principal outstanding ( 1 + rate per month) ^ no of payments made - monthly payment * [(1+ rate per month)^no of payment made - 1]/rate per month
= $200,000 * ( 1+0.04/12)^24 - $955 * [ (1+0.04)^24 - 1]/(0.04/12)
= $192,812

interest rate at beginning at year 3 = min(previous rate + 5%, composite rate) = min (4+5%,7%) = 7%
No of payments outstanding = 28*12 = 336
Monthly payment = Principal outstanding * rate per month * [((1 + rate per month) ^ number of payment)/(((1 + rate per month) ^ number of payment) - 1)
= $192,812 *0.07/12 * [(1 + 0.07/12)^336/((1 + 0.07/12)^336 -1) = $1,310

Principal outstanding at end of year 3 = Principal outstanding ( 1 + rate per month) ^ no of payments made - monthly payment * [(1+ rate per month)^no of payment made - 1]/rate per month
= $192,812 * ( 1+0.07/12)^12 - $1,310 * [ (1+0.07)^12 - 1]/(0.07/12)
= $190,512