Business studies
Discounting a bill of exchange or an invoice
Enter the face value, the rate and the days to maturity: get the bank and the true discount, the present value and what the bank actually credits after its fees.
Bank discount and true discount
Discounting a bill or an invoice means receiving its amount today, before it falls due, and leaving the bank a discount. The bank (commercial) discount is computed on the face value: D = N × rate × days ÷ 360 on the commercial year. On 10,000 at 6% for 90 days, the discount is 150.
The true (rational) discount is computed on the present value, the sum actually advanced, and is always a little smaller: 147.78 in the example. It is the one consistent with simple interest; the bank discount is simpler and favours the lender.
The bank adds fixed and collection fees: with 5 plus 0.1% the net proceeds fall to 9,835, and the effective cost of the operation, measured on what is received, rises above 6.7% a year. That is the rate to compare with other forms of finance.
Common mistakes
- Mixing up bank and true discount: the first is computed on the face value, the second on the present value.
- Forgetting the extra bank days that some banks add to the actual term.
- Judging the discount on the quoted rate alone: fees raise the effective cost.
Frequently asked questions
Why use a 360-day year?
It is the commercial year convention, still used for discounting and many bank calculations: it simplifies the arithmetic and, at the same rate, earns the lender a little more.
How does discounting differ from invoice finance?
In discounting the bank buys the receivable and keeps the discount at once; in invoice finance it lends a percentage of the invoice and charges interest like an overdraft. Either way, compare the effective rate.
What is compound discount?
The discount consistent with compound interest: the present value is N ÷ (1 + i)^t. It is used for long terms, beyond a year.
How this calculation works
With t = days ÷ 360 (or 365) and i the annual rate: bank discount = N × i × t; present value = N − discount. True discount = N × i × t ÷ (1 + i × t). Compound present value = N ÷ (1 + i)^t. Net proceeds = N − bank discount − fees. Effective rate = (N − net proceeds) ÷ net proceeds ÷ t.
Related calculators
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Interest on an invoice or a debt paid late, from the days overdue and the rate.
Simple interest
Solve for capital, rate, periods or final amount when interest is not capitalised.