You have taken out a $300,000, 5/1 ARM. The initial rate of 5.4% (annual) is locked in for 5 years.

You have taken out a $300,000, 5/1 ARM. The initial rate of 5.4% (annual) is locked in for 5 years. Calculate the payment after recasting the loan (i.e., after the reset) assuming the interest rate after the initial lock period is 8.0%. (Note: the term on this 5/1 ARM is 30 years)

A. $1,684.59

B. $1,784.79

C. $1,887.75

D. $2,138.02

Expert Solution

We first calculate the loan amount outstanding after the 5 year period, using the formulae below:

Loan Balance _?k_years? = P [ (1+r)^?t? - (1+r)^?k?] / [(1+r)^t - 1] ; where P is the original loan amount, r is the monthly interest rate, t is the loan tenure in months and k is the number of months after which we are calculating the loan balance. Hence, in this case P = $300,000 , t = (30*12) months = 360 months , k = (5*12) months = 60 months and r = (5.4%/12) since we are calculating the remaining loan balance after the first 5 year period where in the interest was fixed at 5.4%.

Loan Balance _{5 years}? = 300000 * [(1+0.45%)³⁶⁰ - (1+0.45%)⁶⁰] / [(1+0.45%)^?360? - 1] = $ 277,011.92

Now we can calculate the monthly loan repayment for this remaining loan balance at 8% annual rate, with 25 year remaining tenure using the following formulae:

Monthly Payment (MP) = P [r * (1+r)^?t?] / [(1+r)^t? - 1]; r now will be (8%/12) and t will be (25*12) months.

Plugging in the values we get = 277011.92 * [0.67% * (1+0.67%)³⁰⁰] / [(1+0.67%)³⁰⁰ - 1] = $ 2,138.02

Hence answer is option (D).

jeff jeffy answered 2 years ago

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