A 5/1 Hybrid Adjustable Mortgage Plan. Suppose that you finance a home on the basis of a 5/1 hybrid mortgage (five-year fixed/adjustable) plan over 30 years. The $100,000 hybrid loan plan offers an initial rate of 6.02% fixed for 60 months. The loan rate would be adjusted thereafter every 12

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A 5/1 Hybrid Adjustable Mortgage Plan

Suppose that you finance a home on the basis of a 5/1 hybrid mortgage (five-year fixed/adjustable) plan over 30 years. The $100,000 hybrid loan plan offers an initial rate of 6.02% fixed for 60 months. The loan rate would be adjusted thereafter every 12 months to the lowest of three options: the then-current rate on one-year Treasury bills plus 2.75 percent (margin), the previous rate plus a maximum annual cap of 2.0 percent, or a lifetime cap of 11.02 percent. There is no prepayment penalty for this type of loan. The projected interest rates by the lender after five years are as follows.

Projected APR	Period
6.02% (fixed)	Years 1–5
6.45%	Year 6
6.60%	Year 7
6.80%	Year 8
7.15%	Year 9
7.30%	Year 10

(a) Develop the payment schedule for the first 10 years.
(b) Determine the total interest paid over a 10-year ownership.

Accepted Answer

Given: Varying annual mortgage rates and N = 30 years.
Find: (a) The monthly payment and (b) the total interest payment over the 10-year ownership of the home.

(a) Monthly payment calculation. During the first five years, you borrow $100,000 for 30 years at 6.02%. To compute the monthly payment, use i = 6.02%/12 = 0.5017% per month and N = 360 months:

[latex]A_{1 - 60}[/latex] = $100,000(A/P, 0.5017%, 360) = $600.84

The balance remaining on the loan after you make the 60th payment will be

[latex]B_{60}[/latex] = $600.84(P/A, 0.5017%, 300) = $93,074

During the sixth year, the interest rate changes to 6.45%, or 0.5375% per month, but the remaining term is only 300 months. Therefore, the new monthly payment would be

[latex]A_{60 - 72}[/latex] = $93,074(A/P, 0.5375%, 300) = $625.54

After you make the 72nd payment, the balance remaining on the mortgage is

[latex]B_{72}[/latex] = $625.54(P/A, 0.5375%, 288) = $91,5261

During the seventh year, the interest rate changes to 6.60%, or 0.5500% per month. The new monthly payment and the remaining balance after you make the 84th payment are then

[latex]A_{73 - 84}[/latex] = $91,526(A/P, 0.5500%, 288) = $634.03

and

[latex]B_{84}[/latex] = $634.03(P/A, 0.5500%, 276) = $89,908

You can compute the monthly payments in the same fashion for the remaining years. Table 4.7 gives the details over the life of the loan.

(b) To determine the total interest paid over 10 years, we first determine the total monthly mortgage payments over 10 years. Since we know the ending balance at the end of 10 years, we can easily calculate the interest payments during this home ownership period:

Total mortgage payment = 60 [latex] imes[/latex] $600.84

+ 12 ( $625.54 + $634.03 + $645.09 +$664.09 + $672.05 )

= $74,940

Interest payment = Ending balance + Total mortgage payment - $100,000
= $84,704 + $74,940 - $100,000
= $59,644

Table 4.7 Monthly Payments Under 5/1 Hybrid Mortgage

Ending Loan Balance	Monthly Payment	Forecast Rate	Month	Year
$98,777	$600.84	6.02%	1–12	1	Fixed rate
$97,477	$600.84	6.02%	13–24	2
$96,098	$600.84	6.02%	25–36	3
$94,633	$600.84	6.02%	37–48	4
$93,074	$600.84	6.02%	49–60	5
$91,526	$625.54	6.45%	61–72	6	Variable rate
$89,908	$634.03	6.60%	73–84	7
$88,229	$645.09	6.80%	85–96	8
$86,513	$664.09	7.15%	97–108	9
$84,704	$672.05	7.30%	109–120	10

Question 4.20: A 5/1 Hybrid Adjustable Mortgage Plan. Suppose that you fina...

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