Question

In: Finance

2.Assume the following for a one-year rate adjustable rate mortgage loan that is tied to the...

2.Assume the following for a one-year rate adjustable rate mortgage loan that is tied to the one-year Treasury rate: Loan amount: $200,000 Annual rate cap: 1% Life-of-loan cap: 4% Margin : 2.50% First-year teaser rate: 5.50% One-year Treasury rate at end of year 1: 5.25% One-year Treasury rate at end of year 2: 5.50% Loan term in years: 15 Given these assumptions, calculate the following: a.Initial monthly payment b.Loan balance end of year 1 c.Year 2 contract rate d.Year 2 monthly payment e.Loan balance end of year 2 f.Year 3 contract rate g.Year 3 payment

Solutions

Expert Solution

a. Loan amount = $200,000

Annual rate = 5.50 %

Tenure = 15 years

EMI = Loan amount * (annual rate/12) * [((1 + annula rate/12) ^ number of payment)/(((1 + annula rate/12) ^ number of payment-1)

= $200,000 * 0.055/12 * [(1 + 0.055/12) ^ 180]/[(1+0.055/12)^18 -1] = $1,634

b. Remaining Balance = [Loan amount * (1+ annual rate/12)^number of payment done] - Monthly payment * [ ((1+ annual rate/12)^number of payment done - 1)/(annual rate/12)]

= [$200,000 * (1+0.055/12)^12] - $1,643 * [ ((1 + 0.055/12)^12 - 1)/(0.055/12)] = $191,101

c. year 2 contract rate = max( (Treasure rate at end of year 1 + margin), ( first year teaser rate + annual rate cap))

= max ( (5.25 + 2.50), (5.50 + 1)) = 6.50

d. Loan amount = $191,101
annual rate = 6.50%

tenure = 14 years

EMI = Loan amount * (annual rate/12) * [((1 + annula rate/12) ^ number of payment)/(((1 + annula rate/12) ^ number of payment-1)

= $191,101 (0.065/12) * [((1 + 0.065/12) ^ 168)/((1 + 0.065/12) ^168 -1)] = $1,735

e.

Remaining Balance = [Loan amount * (1+ annual rate/12)^number of payment done] - Monthly payment * [ ((1+ annual rate/12)^number of payment done - 1)/(annual rate/12)]

= [$191,101 * (1+0.065/12)^12] - $1,735 * [ ((1 + 0.065/12)^12 - 1)/(0.065/12)] = $182,409

f. year 3 contract rate = max( (Treasure rate at end of year 2 + margin), ( secont year rate + annual rate cap))

= max ( (5.50 + 2.50), (6.50 + 1)) = 7.50

g.

Loan amount = $182,409

Annual rate = 7.50%

Tenure = 13 years

EMI = Loan amount * (annual rate/12) * [((1 + annula rate/12) ^ number of payment)/(((1 + annula rate/12) ^ number of payment-1)

= $182,409 (0.075/12) * [((1 + 0.075/12) ^ 156)/((1 + 0.075/12) ^156 -1)] = $1,834


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