Lesson 10 of 25 · 7 min

What a rate change does to a balance that is capitalising

Unpaid interest joins the principal, so a rising path charges its highest rates against the largest balance it created.

A rate rise on a facility where interest is paid each month costs the rate times the balance, and that is the whole of it. On a facility where interest is capitalised it costs more than that, and the excess grows with the length of the path.

The mechanism is ordinary compounding with one extra feature. Each month's interest is added to the balance, so the following month charges a higher rate against a larger number. A rising rate and a rising balance are not two independent problems; they multiply.

Take $645,000 drawn and never repaid, Act/360, across 730 days. Held flat at 6.20 percent, the balance ends at $731,168.64, a growth of 13.36 percent. On a path rising in even monthly steps from 6.20 percent to 9.05 percent — an average of 7.625 percent — it ends at $752,522.15, a growth of 16.67 percent. The rate path added $21,353.51.

Separate out the compounding itself. Had every month's interest been paid rather than capitalised, the same rate path on a constant $645,000 would have cost $99,770.83. Capitalised, it cost $107,522.15. The $7,751.32 difference is compounding alone — 7.77 percent more interest for the identical rate path, produced entirely by not paying it.

That larger balance is the numerator of every headroom calculation. With collateral flat at $1,340,000 and a threshold of 70 percent of market value, the trigger value starts at 645,000 ÷ 0.70 = $921,428.57 and ends at 752,522.15 ÷ 0.70 = $1,075,031.64. Headroom falls from 31.24 percent to 19.77 percent — 11.46 points surrendered across two years in which the market did nothing whatsoever.

Key terms

Path dependence: The property that a total depends on the order in which rates arrived, not only on their average. Late high rates cost more than early ones.
Compounding drag: The extra interest produced by leaving interest unpaid, over and above the same rate path on a constant balance.
Flat-market headroom loss: Headroom given up purely through balance growth, with no move in collateral value at all.

Worked example

Two years of accrual on $645,000

Drawn once and never repaid. Act/360, 730 days, collateral flat at $1,340,000, threshold 70 percent of market value.

Flat at 6.20%, ending balance: $731,168.64
Rising from 6.20% to 9.05%, ending balance: $752,522.15
Same path with interest paid monthly: $99,770.83 of interest
Same path with interest capitalised: $107,522.15 of interest
Trigger value, start and end: $921,428.57 and $1,075,031.64
Headroom, start and end: 31.24% and 19.77%

Nothing happened to the market across two years. Eleven and a half points of headroom went anyway, because the numerator is the only term in the ratio that has a direction.

Check yourself

Two facilities follow the identical rate path from 6.20 percent to 9.05 percent over two years on an identical $645,000. One pays interest monthly and one capitalises it. What separates their total interest, and why is the difference not zero?

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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.