ARM caps and indexes

Adjustable-rate questions are arithmetic questions in disguise. Get the mechanism and they become easy marks.

The formula

Fully indexed rate equals index plus margin.

The index moves with the market and the lender does not control it. The margin is fixed for the life of the loan and is the lender's. Add them and you have the rate the loan wants to charge. Apply the cap last.

Then the caps limit it

A 2/2/5 structure means two percentage points at first adjustment, two at each one after, and five over the life of the loan.

A worked example

Start rate 4 percent, 2/2/5 caps, index at first adjustment 5 percent, margin 3 percent.

Fully indexed rate is 8 percent. But the initial cap allows only 2 points of movement, so the rate goes to 6 percent, not 8.

Hybrids

A 5/1 ARM is fixed for five years then adjusts annually. The first number is the fixed period in years and the second is the adjustment frequency.

Do not confuse the 5/1 notation with the 2/2/5 cap notation. They describe different things and appear in the same question.

How the adjustment date and index value fit in

The note specifies when the first adjustment occurs, how often later adjustments occur, and which published index value is used. The fully indexed rate uses that contractually selected index at its measurement date, plus the margin. Do not substitute a current headline rate or assume the lender can choose a different benchmark when the loan adjusts. The contract's lookback and rounding provisions can affect the exact number in a real loan.

Apply each cap from the right reference rate

An initial adjustment cap measures the first rate change against the rate stated as its reference in the loan terms. A periodic cap limits a later single adjustment, usually relative to the rate in effect immediately before it. A lifetime cap limits the total change from the original rate over the loan. Calculate index plus margin first, then compare that target with each applicable limit. If the question supplies a floor as well, check the lower limit too.

For example, with a 5% starting rate, a 2-point initial cap, and a 9% fully indexed rate at the first adjustment, the initial cap would limit the rate to 7% if the contract uses the starting rate as its reference and no other term changes the result. At a later adjustment, a 2-point periodic cap is measured from the then-current rate, not automatically from the original introductory rate.

From the new rate to the new payment

A rate adjustment and a payment adjustment are related but not interchangeable. For a typical fully amortizing ARM, the servicer recalculates the principal-and-interest payment using the new rate, outstanding principal, and remaining amortization term. Escrow for taxes and insurance is separate and can change even when principal and interest do not. Some products use payment limits or negative-amortization features, so follow the loan terms given in the question rather than assuming the payment always tracks the rate immediately.

A step-by-step exam calculation

• Mark the current index and contractual margin; add them to get the fully indexed rate.
• Identify whether the question is about the initial, a later periodic, or the lifetime cap.
• Apply that limit from the correct reference rate, then check any floor.
• If asked for a payment, use the resulting rate with the current balance and remaining term; do not confuse the payment with total PITI.