Break-even discount
2.70%
Discount vs Installment Calculator
Compare a single discounted payment against interest-free installments using a break-even discount estimate.
Key Terms (Click to expand)
Cash discount
The percent reduction offered when you pay the full price up front.
Interest-free installments
Equal payments that add up to the original price with no explicit finance charge.
Present value
The current value of future installment payments after applying your assumed return rate.
Break-even discount
The cash discount needed for paying now to match the installment plan's present value.
Tool
The discounted single payment is better under these assumptions.
Discounted cash price
$1,140.00
Installments present value
$1,167.65
Discount vs installment detail
| Installment amount | $120.00 |
|---|---|
| Installment count | 10 |
| Annual return assumption | 6.00% |
| Monthly opportunity rate | 0.500% |
| Value difference | $27.65 |
Methodology
The calculator compares the discounted cash price with the present value of equal interest-free payments.
- Cash price: purchase price multiplied by one minus the cash discount.
- Monthly opportunity rate: annual return rate divided by 12.
- Installment present value: each installment discounted back to today by payment month.
- Break-even discount: one minus installment present value divided by purchase price.
Worked Example
For a purchase price of $1,200, the cash discount needs to be at least 2.70% to match 10 interest-free installments under the selected return assumption.
Assumptions and Limitations
- The annual return rate is a planning assumption for money you keep while paying installments.
- Installments are modeled as equal payments with no fees or explicit interest.
- Taxes, rewards points, card fees, inflation, and liquidity needs are not included.
FAQ
Why does the annual return rate matter?
It estimates the value of keeping money longer while paying no-interest installments.
What does break-even discount mean?
It is the cash discount needed for paying now to equal the installment plan's present value.
Does this include rewards or card fees?
No. It compares cash discount and installment timing only, using the assumptions shown.