Break-even discount
2.70%
Discount vs Installment Calculator
Compare a cash discount today against an interest-free installment plan in present-value terms and see which option truly costs less. Math shown. No sign-up.
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 premises.
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 premise | 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.
Using This Tool Well
When to use this tool
- Checkout decision: compare a $1,200 purchase with a 5% cash discount against 10 interest-free installments before choosing convenience over price.
- Hurdle-rate check: use the table result to see whether your idle cash can realistically beat the implied rate created by skipping the discount.
- Payment-stack audit: add the new installment to active plans so a $120 monthly payment is judged against the total committed outflow, not in isolation.
How to read the result
The break-even discount is the threshold. If the actual discount is higher, cash is cheaper in present-value terms. If it is lower, installments only win when the retained cash truly stays available and earns the return you entered.
Common mistakes
- Treating kept cash as spare cash: in the $1,200 example, the $60 skipped discount still costs money if the retained cash is spent instead of preserved.
- Ignoring the hurdle rate: a 5% discount over 10 installments beats a 6% idle-cash return by about $27.65 in present-value terms in the guide scenario.
- Forgetting fees: a $4 processing fee on each of 10 payments adds $40, which can erase most of the apparent installment benefit on a small purchase.
Reviewed by Leonardo, Software Engineer
Last reviewed June 23, 2026
Premises and Limitations
- The annual return rate is a planning premise 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 premises shown.