Lesson 12 of 25 · 6 min

A repayment mid-period

A repayment cuts the balance on the day it posts, and every later day is a different product.

Now the other direction, and on a different date, so the split is not a mirror of the draw. Invent a $63,400 repayment posted on 8 March, still against the Halden & Wren rates. The reset is 12 March, so the repayment lands inside period 1. The month again has three constant stretches: seven days on the old balance at 6.97 percent, four days on the reduced balance at 6.97 percent, then twenty days on the reduced balance at 7.22 percent. 7 + 4 + 20 = 31.

The reduced balance is $1,847,220 − $63,400 = $1,783,820. First leg: $1,847,220 × 0.0697 × 7 ÷ 360 = $2,503.496216…, which prints as $2,503.50. Second: $1,783,820 × 0.0697 × 4 ÷ 360 = $1,381.469488…, which prints as $1,381.47. Third: $1,783,820 × 0.0722 × 20 ÷ 360 = $7,155.100222…, which prints as $7,155.10. The month totals $11,040.07.

Against the sample $11,343.47 the repayment saved $303.40. That saving is the $63,400 that no longer sits in the later products: $63,400 × 0.0697 × 4 ÷ 360 + $63,400 × 0.0722 × 20 ÷ 360 = $49.10 + $254.30 = $303.40. Four days of the old rate and twenty days of the new one, on the repaid principal only.

The close is $1,783,820 + $11,040.07 = $1,794,860.07. Notice the date. A repayment on the 8th, before the reset, cuts both remaining rate stretches. The 19 March draw in the previous lesson cut only the last twelve days at 7.22 percent. Same four-factor rule; the calendar decides how many products change.

Key terms

Repayment: A posting that lowers the outstanding balance on a stated date. Later legs use the reduced figure; earlier legs do not.
Saved product: The interest the repaid principal would have earned over the remaining days. Here $303.40 on $63,400.

Worked example

Eight March, $63,400 repaid

Same March rates as the sample. Repayment $63,400 on 8 March, so the later balance is $1,783,820.

7 days × $1,847,220 × 6.97%: $2,503.50
4 days × $1,783,820 × 6.97%: $1,381.47
20 days × $1,783,820 × 7.22%: $7,155.10
Month with the repayment: $11,040.07
Saved against the sample month: $303.40
Closing balance: $1,794,860.07

The $63,400 leaves the products from 8 March onward. The first seven days are the sample's period 1, cut short.

Check yourself

A $63,400 repayment on 8 March leaves $1,783,820 outstanding. What are the three legs, and what does the month total?

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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.