Hong Life CalculatorsUnderstanding the installment plan real cost calculator — concept and principle
Paying in instalments spreads a purchase over months, but interest and fees can make it noticeably more expensive than paying cash. This calculator works out the fixed monthly payment of a standard amortising plan, the total you will pay, and the extra cost compared with the cash price, so you can decide whether the convenience is worth it.
How it is calculated
- Monthly rate: r = APR ÷ 12 ÷ 100.
- Monthly payment = P × r ÷ (1 − (1 + r)^−n), where P is the price and n the number of months. If the APR is 0, the payment is simply P ÷ n.
- Total paid = monthly payment × n + upfront fee.
- Extra cost = total paid − price.
The principle
Each payment first covers the interest on the balance still owed, and the rest reduces the balance. Early payments therefore contain more interest and later ones more principal, while the payment itself stays the same. The formula above is the payment that makes the present value of n equal payments, discounted at rate r, exactly equal the price; it is the same annuity formula used for car loans and mortgages. An upfront fee is added separately because it is paid once, not spread over the months.
Worked example
- Inputs: price $1,200, 12 months, APR 15%, no fee.
- Monthly rate: 15 ÷ 1200 = 0.0125 (1.25%).
- Payment: 1200 × 0.0125 ÷ (1 − 1.0125^−12) = $108.31.
- Total paid: 108.31 × 12 + 0 = $1,299.72.
- Extra cost: 1,299.72 − 1,200 = $99.72.
In the first month, interest is 1,200 × 0.0125 = $15.00 and $93.31 goes towards the balance.
| Months | Monthly payment |
|---|---|
| 3 | $410.04 |
| 6 | $208.84 |
| 9 | $141.80 |
| 12 | $108.31 |
| 15 | $88.23 |
| 18 | $74.86 |
| 24 | $58.18 |
How to read the result
The extra cost is the price of borrowing. Compare it with alternatives: saving for a few months, a cheaper loan, or a cash discount. Note that 15% APR over one year costs about 8.3% of the price, not 15%, because the balance shrinks as you pay. A "0% interest" plan with a fee is not free: a $30 fee on $1,200 over 12 months is a real cost of 2.5% of the price.
Common mistakes
- Comparing only monthly payments; a longer term lowers the payment but raises the total.
- Ignoring upfront, admin or monthly account fees.
- Assuming a 0% promotion stays 0%; some plans charge back-dated interest if one payment is late or the balance is not cleared in time.
- Forgetting the cash discount you might get by paying in full.
Frequently asked questions
What is the difference between APR and the monthly rate?
APR is the yearly rate quoted; this calculator divides it by 12 to get the monthly rate applied to the balance.
Is paying off early cheaper?
Usually, because interest is charged only on the outstanding balance, but some contracts have early repayment charges.
Why is the extra cost less than 15% of the price?
You repay part of the balance every month, so on average you owe only a little more than half the price over the year.
Sources: Consumer Financial Protection Bureau — Truth in Lending (Regulation Z), APR and finance charge disclosures · Brealey, Myers & Allen — Principles of Corporate Finance (annuity present value)