Purchase repayments and total cost
Read the terms before calculating. These fictional models have no other fees or charges, so total paid above cash price is interest
- Define the quantities C is cash price, D deposit, m one repayment, n repayment count, S all instalments, T total paid and I interest. Money is in dollars. The percentage number p is applied to C.
- Deposit and instalments Count every repayment. This model uses 12 monthly or 26 fortnightly repayments per year; actual calendar schedules may differ \(\displaystyle \begin{gathered}D=(p/100)C\\S=mn\end{gathered}\)
- Whole cost and extra cost Add the deposit only once. Subtract cash price to find the extra cost. Here there are no other fees or charges, so the extra cost is interest \(\displaystyle \begin{gathered}T=D+S\\I=T-C\end{gathered}\)
Worked example
A $2,400 camera has a 20% deposit followed by 12 monthly repayments of $190. There are no other fees or charges. Find the deposit, instalment total, total paid and interest
- \(\displaystyle D=0.20(2400)=\$480\)Apply the deposit percentage to cash price
- \(\displaystyle S=12(190)=\$2{,}280\)Count all twelve instalments
- \(\displaystyle T=480+2280=\$2{,}760\)Include the separate deposit
- \(\displaystyle I=2760-2400=\$360\)Remove cash price once to find interest in this fee-free model
Common mistakes
Difficulty levels
Questions about this topic
Why multiply years by 26 for fortnightly payments?+
That is the explicit model-year convention in these questions. Real payment dates may produce a different count, so use the actual schedule when one is supplied
Does a lower regular payment mean a cheaper purchase?+
No. A longer term can produce a larger total even when each repayment is smaller. Compare both the whole cost and the budget constraint
Is extra cost always interest?+
Only under the stated no-other-fees assumption. Otherwise total paid minus cash price can contain fees as well as interest
Should the deposit be deducted from total instalments?+
No. The deposit and instalments are separate amounts paid. Add them to find total paid
Can I use a calculator?+
A calculator is allowed unless a question is marked no calculator
Which year level and chapter is this?+
Year 10 Mathematics, chapter 2: Consumer arithmetic