How to use it
- Type the Price before the cash discount and the Cash discount, %.
- Type the Number of monthly installments and the Total fee or interest on the plan, %, or 0.
- Type the Monthly rate you keep money at, %, and choose when the First installment is paid.
- Read Cheaper today and the Difference in today's money, then the table of payments and their present values.
How the present value of installments is calculated
Money paid later is worth less today, because the cash could have been kept and earned a return in the meantime. The present value of a payment is the amount you would need to keep today at the monthly rate to cover it on time. Wikipedia gives the present value of a single sum as C × (1 + i)^(−n), and the same discounting applied to equal payments is an annuity.
The installments add up to the list price plus the fee on the plan. The cash price is the list price less the cash discount. Each present value is rounded to the cent, and the total is the sum of the rounded values.
Cash price = list price × (1 − cash discount)
Installments total = list price × (1 + fee)
Present value = Σ installment ÷ (1 + i)^t, where t is the month the installment is paid
Difference = cash price − present value of the installments- For 1,200 with 12 installments of 100 and a monthly rate of 2%: the first is paid a month later, so the present values are 100 ÷ 1.02 = 98.04, then 100 ÷ 1.02² = 96.12, and so on, adding up to 1,057.54 for the 12 payments.
- Cash after a 5% discount is 1,140.00, so the installments are worth 82.46 less today and are the cheaper choice at 2% a month.
Cash, the fee and the break-even rate
Paying cash spends money you could have kept invested. Wikipedia defines opportunity cost as the value of the best alternative that is given up. The monthly rate you enter is that alternative: the higher it is, the more the installments are worth against cash.
The break-even rate is the monthly rate at which the present value of the installments equals the cash price. If the installments add up to more than the cash price, a break-even rate exists: above it the installments cost less today, below it the cash does. If they add up to no more than the cash price, the installments are never dearer.
What this calculator does not include
- A fee that changes month by month. Enter the total of all the fees on the plan as one percentage.
- Taxes, insurance, delivery and the seller's warranty, which may differ between the two options.
- A monthly rate that changes over the months. Use one rate for the whole plan.
Worked example: 1,200 in 12 installments, or cash after 5% off, at 2% a month
The cash price is 1,200 less 5%, which is 1,140.00. The installments add up to 1,200 with no fee, so each one is 100.00 and the first is paid a month after buying.
At 2% a month the twelve installments are worth 1,057.54 today. That is 82.46 less than the cash price, so the installments are cheaper today. The break-even monthly rate is about 0.80%: above it the installments remain cheaper, below it cash is cheaper.
| Item | Figure |
|---|---|
| Cash price after 5% off | 1,140.00 |
| Installments, total | 1,200.00 |
| Installments, present value at 2% a month | 1,057.54 |
| Cheaper today by | 82.46 (installments) |
Frequently asked questions
Are installments always more expensive than cash?
No. Installments cost more today only when their total, after the fee, is above the cash price and the rate you keep money at is low. Compare the present value with the cash price at your own rate.
Which monthly rate should I enter?
Enter the monthly return you could really earn on the cash, such as a deposit or savings rate, or the monthly inflation you expect. A higher rate makes the installments look cheaper, so use a figure you can get.
Does a plan with no fee cost nothing extra?
Not in money terms: with no fee the installments add up to the list price, but you pay them over time. Their present value is lower, and that gain is the reason an interest-free plan can be worth taking.
What is the break-even rate?
It is the monthly rate at which both options cost the same today. Above it the installments are cheaper; below it cash is cheaper. Use it as a test: if your money would earn more than this rate a month, paying in installments and keeping the cash is the better choice; if it would earn less, paying cash is.
Why does the timing of the first installment matter?
A first payment at the purchase is discounted for no months, so its present value is the full amount. A payment a month later is discounted once, so paying at the purchase makes the installments look dearer.
Is my data sent to a server?
No. The calculation runs in your browser, and nothing you enter is sent to us.
Sources
- Wikipedia: Present value (present value of a sum and of an annuity)
- Wikipedia: Opportunity cost (value of the best alternative given up)
Figures and text last checked on Tuesday, November 10, 2026.