An ARM is made for $150,000 for 30 years with the following terms: Initial inter

ID: 2776912 • Letter: A

Question

An ARM is made for $150,000 for 30 years with the following terms:

Initial interest rate = 7 percent

Index = 1-year Treasuries

Payments reset each year

Margin = 2 percent

Interest rate cap = none

Payment cap = 5 percent increase in any year

Fully amortizing, however, negative amortization allowed if payment cap reached. Based on estimated forward rates, the index to which the ARM is tied is focused as follows:

Beginning of year 2 = 7 percent

Beginning of year 3 = 8.5 percent

Compute the uncapped and capped payments, end of year loan balances.

Compute the uncapped and capped payments, loan balances, and yield for an ARM that has a maximum 5% annual payment cap and does allow negative amortization.

Principal = $150,000

Term = 30 years

Margin = 2.00%

Initial Rate 7.0%

Explanation / Answer

Principal = $150,000

Term = 30 years

Margin = 2.00%

Initial Rate = 7.0%

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BOY

Uncapped Rate

Payment

Monthly Interest

Monthly Amort

Annual Amort.

Year

Balance

Uncapped

Capped

$150,000

7.00%

$997.95

$875.00

$122.95

$1,475.44

$148,525

9.00%

$1,203.28

$1,047.85

$1,113.93

($66.08)

($792.99)

$149,318

10.50%

$1,380.45

$1,100.24

$1,306.53

($206.28)

($2,475.41)

$151,793

11.50%

$1,524.01

$1,155.26

$1,454.68

($299.43)

($3,593.12)

$155,386

13.00%

$1,743.81

$1,213.02

$1,683.35

($470.33)

($5,643.96)

$161,030

Calculator:

PV = -$147,000

PMT = 997.95 N = 12

PMT = 1047.85 N = 12

PMT = 1100.24 N = 12

PMT = 1155.26 N = 12

PMT = 1213.02 N = 11

PMT = 1213.02 + 161,030 N = 1

Solve for the annual IRR:

1 = 0.8648% (x 12) = 10.38%

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BOY