What this calculator does
This is a general consumer loyalty-program tool. When you buy an item and pay part of the price with existing reward points, it works out how much you pay in cash, how much you pay with points, how many new points you earn, and the effective point rate of the whole transaction. It uses generic "currency units" shown as yen, where 1 point equals 1 currency unit, but it works for any currency.
How to use it
Enter the item's sticker price, the point rate (the reward percentage the purchase normally earns), and the amount of points you want to apply. The calculator clamps points to the price (you cannot redeem more than the item costs) and returns all four figures instantly.
The formula explained
Let S be the price, r the point rate as a fraction, and P the points used. Points pay \(\text{pointPayment} = \min(P, S)\), cash covers \(\text{cashPayment} = \max(S - P, 0)\). Crucially, most point programs grant new points only on the cash portion, so \(\text{newPoints} = \text{cashPayment} \times r\). The effective rate is \(\left(\text{newPoints} / S\right) \times 100\) - the share of the full price you actually get back as points.
$$\begin{gathered} \text{Cash Payment} = \text{Price} - \min\!\left(\text{Points Used},\ \text{Price}\right) \\[1.5em] \text{New Points Earned} = \text{Cash Payment} \times \dfrac{\text{Point Rate (\%)}}{100} \end{gathered}$$
Worked example
Price 3000, point rate 10% (\(r = 0.10\)), points used 1000. Points payment = 1000, cash payment = 2000, new points:
$$\text{new points} = 2000 \times 0.10 = 200$$effective rate:
$$\frac{200}{3000} \times 100 = 6.67\%$$Although the nominal rate is 10%, redeeming 1000 points dropped the realized rate to just 6.67%.
FAQ
Why is the effective rate below the point rate? Because new points accrue only on cash spent. Spending points shrinks the cash portion, so fewer new points are earned relative to the full price.
What is the smart strategy? Spend points on items that earn no points or have a low point rate. Using points on a high-rate item forfeits the new points you would have earned on that cash.
What if points exceed the price? The points payment is capped at the price, cash becomes 0, and no new points are earned.
