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%

This is the Solution -

Year BOY Payment EOY

Year Balance Uncapped Capped Balance

1 $150,000 $997.95 $997.95 $148,476

2 $148,476 $1,202.89 $1,047.85 $149,298

3 $149,298 $1,380.27 $1,100.24 $151,894

Can someone please explain to me how one would mathematically go about calculating these values for the first 3 years?