Financial Accounting · Hire Purchase and Installment Sale Transactions

Calculation of Interest and Installment Amounts in Hire Purchase

Updated 10 October 2026 · Fact-checked

In hire purchase, each installment contains part interest and part principal. Total interest equals total hire purchase price minus cash price. Interest for a year is charged on the outstanding cash price balance at the start of that period. The principal part of the installment is the installment minus that interest.

Understand Calculation of Interest and Installment Amounts

A hire purchase seller gives you goods now and collects the price in installments. The installments add up to more than the cash price. The extra amount is interest, the seller's charge for waiting for the money.

Every installment has two parts. One part is interest on the amount still unpaid. The other part repays the cash price. As you pay, the unpaid balance falls, so the interest part falls and the principal part rises.

This is the outstanding balance method. Interest for a period is the rate multiplied by the balance outstanding at the start of that period. Then you subtract the principal part from the balance to get the new balance.

There are three typical questions. First, given the cash price and installments, split the interest year by year. Second, given the installments and the rate, work backwards to the cash price. Third, given the cash price and installments, find the rate. The cash down payment, if any, is paid at the start. It carries no interest and reduces the balance on which interest is charged.

Key rules to remember

Total interest: Total interest = Total hire purchase price − Cash price; Total hire purchase price = down payment + all installments.
Interest for a period: Interest = Outstanding balance at start of period × Rate × Time; Use the balance after the previous installment is paid. For a half-year, time is 6/12.
Principal part of an installment: Principal = Installment − Interest; Deduct this from the opening balance to get the closing balance.
Interest in the last installment: Interest in last installment = Last installment − Opening balance; The final balance must clear to nil, so the last interest is a balancing figure.
Interest in the last installment when the rate is given: Interest in last year = Last installment × r ÷ (100 + r); Here r is the yearly rate in percent and the installment is paid at year end. For example, ₹1,10,000 × 10 ÷ 110 = ₹10,000.
Cash price from installments (rate given): Cash price = Down payment + Σ [Installment ÷ (1 + r)^n]; Equivalent to working back from the last installment. Opening balance = (closing balance + installment) ÷ (1 + r) at each step.

How to solve Calculation of Interest and Installment Amounts questions

Use this order for any question on interest, cash price or rate. First decide which figure is missing, then pick the direction of working.

1Write the data: cash price, down payment, installments, dates, rate and whether payments are at year end or start.
2Subtract the down payment from the cash price to get the balance on which interest runs. If the cash price is not given, mark it as the unknown.
3If the cash price and installments are known, calculate total interest, then split it year by year: interest = opening balance × rate.
4Prepare a schedule with columns: year, opening balance, interest, installment, principal repaid, closing balance. Check that the last closing balance is nil.
5If the cash price is unknown and the rate is given, start from the last installment. Its opening balance = installment × 100 ÷ (100 + rate). For each earlier year, the closing balance plus that year's installment equals the opening balance with that year's interest included. So opening balance = (closing balance + installment) × 100 ÷ (100 + rate). Repeat back to year 1.
6If the rate is unknown, use the given interest or schedule data. Interest ÷ opening balance gives the rate for the period. Convert to a yearly rate if the period is not one year.
7Write the answer with the schedule. Show interest and principal separately, since the next topic, journal entries, uses these figures.

Quickest way: Work backwards from the last installment

When to use it: Use it when the cash price is asked and the installments and rate are given, or when interest in the last year is needed.

Take the last installment. It equals opening balance plus interest, so opening balance = installment × 100 ÷ (100 + rate).
Interest in that year = installment − opening balance.
For the previous year, add that year's installment to the closing balance (the opening balance you just found). This sum is the balance with that year's interest included. So opening balance = (closing balance + installment) × 100 ÷ (100 + rate).
Continue until the first year. Add the down payment to get the cash price.
Verify by running the schedule forward. The final balance must come to nil.

Common mistakes in Calculation of Interest and Installment Amounts

Charging interest on the original cash price every year.
Students forget that principal is repaid with every installment.
Fix: Always take interest on the opening balance of that period, after the previous installment.
Charging interest on the down payment.
The down payment is treated like any other payment.
Fix: Deduct the down payment from the cash price first. Interest runs only on the balance.
Dividing total interest equally across the years.
It is easy and looks neat.
Fix: Equal division is wrong under the outstanding balance method. Interest falls each year as the balance falls, unless the question says to spread it equally.
Computing the last year's interest as rate × opening balance despite rounding differences.
Installments and earlier interest are rounded, so rate × opening balance can differ slightly and the closing balance fails to reach nil.
Fix: Take the last interest as installment minus opening balance. This clears the account exactly.
Using the full-year rate for a half-year installment.
The time period in the question is missed.
Fix: Multiply by the fraction of the year, such as 6/12 for half-yearly payments.

Worked examples

Example 1

Ravi Traders bought a machine from Kaveri Machines on hire purchase. Cash price ₹2,00,000. ₹50,000 is paid on signing the agreement and the balance in three yearly installments of ₹60,317 each, payable at the end of each year. Interest is 10% per annum on the outstanding balance. Prepare the schedule and find the interest included in each installment.

Show the solution

Balance on which interest runs = ₹2,00,000 − ₹50,000 = ₹1,50,000.
Year 1: interest = 10% of ₹1,50,000 = ₹15,000. Principal = ₹60,317 − ₹15,000 = ₹45,317. Closing balance = ₹1,50,000 − ₹45,317 = ₹1,04,683.
Year 2: interest = 10% of ₹1,04,683 = ₹10,468 (rounded). Principal = ₹60,317 − ₹10,468 = ₹49,849. Closing balance = ₹1,04,683 − ₹49,849 = ₹54,834.
Year 3: the closing balance must be nil, so the interest is the balancing figure = installment − opening balance = ₹60,317 − ₹54,834 = ₹5,483. This agrees with 10% of ₹54,834 = ₹5,483 (rounded). Principal = ₹54,834. Closing balance = nil.
Check: total price = ₹50,000 + 3 × ₹60,317 = ₹2,30,951. Total interest = ₹2,30,951 − ₹2,00,000 = ₹30,951.
Sum of yearly interest = ₹15,000 + ₹10,468 + ₹5,483 = ₹30,951. This agrees.

Answer: Interest in the installments: year 1 = ₹15,000, year 2 = ₹10,468, year 3 = ₹5,483. Total interest = ₹30,951. The closing balance after year 3 is nil.

Example 2

Meera Textiles purchased equipment on hire purchase from Sundaram Ltd. The price is payable in three yearly installments of ₹1,10,000 each at the end of each year, with no down payment. Interest is 10% per annum. Find the cash price and the interest included in each installment.

Show the solution

Work from the last installment. Opening balance of year 3 = ₹1,10,000 × 100 ÷ 110 = ₹1,00,000. Interest in year 3 = ₹1,10,000 − ₹1,00,000 = ₹10,000.
Year 2: the balance after year 2's installment is ₹1,00,000. So the opening balance of year 2 = (₹1,00,000 + ₹1,10,000) × 100 ÷ 110 = ₹2,10,000 × 100 ÷ 110 = ₹1,90,909.09 approx.
Interest in year 2 = 10% of ₹1,90,909 = ₹19,091 approx. Check: ₹1,90,909 + ₹19,091 − ₹1,10,000 = ₹1,00,000. This agrees.
Year 1: opening balance = (₹1,90,909 + ₹1,10,000) × 100 ÷ 110 = ₹3,00,909 × 100 ÷ 110 = ₹2,73,554 approx. This is the cash price.
Interest in year 1 = 10% of ₹2,73,554 = ₹27,355 approx.
Total interest = ₹3,30,000 − ₹2,73,554 = ₹56,446. Sum of yearly interest = ₹27,355 + ₹19,091 + ₹10,000 = ₹56,446. This agrees.

Answer: Cash price ≈ ₹2,73,554. Interest in installments: year 1 ≈ ₹27,355, year 2 ≈ ₹19,091, year 3 = ₹10,000. Total interest ≈ ₹56,446.

Exam tips

Build the schedule in a table with opening balance, interest, installment, principal and closing balance. It earns step marks even if one figure slips.
Always check the final closing balance is nil. If it is not, an earlier figure is wrong.
If the question gives total interest but not the rate, find the rate from the first year's interest divided by the opening balance.
Read whether installments fall at the start or the end of the year. This changes the balance on which interest is computed.
For MCQs, the last-installment trick gives the answer in seconds: divide by (100 + rate) and multiply by 100.

Practice questions from Hire Purchase and Installment Sale Transactions

Calculation of Interest and Installment Amounts: frequently asked questions

How do I calculate interest in a hire purchase installment?

Take the outstanding balance at the start of the period and multiply it by the rate and the time. Deduct this interest from the installment to get the principal repaid. Then reduce the balance by the principal.

How do I find the cash price from installments?

If the rate is given, start from the last installment and work backwards. At each step, add that year's installment to the closing balance, then multiply by 100 and divide by (100 + rate) to get the opening balance. For the last year, the closing balance is nil. Add any down payment at the end.

How do I find the rate of interest in hire purchase?

Find the interest for the first period as the opening balance's share of the installment, or use the given interest figure. Divide interest by the opening balance and by the time in years. Check that the schedule clears to nil.

Is interest charged on the down payment?

No. The down payment is paid at the start and carries no interest. Interest runs only on the balance of the cash price after the down payment.