Banking and Loans

How to Work Out a Personal Loan Payment and Its True Cost

Work out a personal loan's monthly payment, what an upfront fee leaves you with, the cost of credit and the annual rate once the fee is counted.

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Editorial dates are calendar dates in India Standard Time.

Keywords

  • personal loan calculator
  • personal loan emi calculator
  • loan calculator with origination fee
  • personal loan apr with fee

The payment is only part of what a personal loan costs

Two personal loans with the same interest rate can cost different amounts, because one charges a fee at the start and the other does not. This guide works through the monthly payment, what an upfront fee does to the cash you receive, the cost of credit, and the single rate that counts both interest and the fee.

Amount borrowed, cash received and cost of credit

A personal loan is a fixed amount repaid by level monthly payments of principal and interest over a set term. An upfront fee, called an origination, processing, arrangement or establishment fee in different markets, is charged once when the loan is set up. When it is taken from the loan, the cash you receive is less than the amount you borrow and pay interest on. The cost of credit is the interest plus the fee.

The interest rate is the price of the money alone. A rate that also counts fees is called the APR in the United States, the United Kingdom, Canada and India, and the comparison rate in Australia. Each has its own legal definition.

Compare offers with different rates and fees

Enter each offer in turn with the same term. The payment shows what leaves your account each month. Cash received shows what you get to spend. The cost of credit and the rate including the fee show which offer is cheaper overall. The chart shows how much is still owed after any month, which matters if you plan to repay early.

A level payment, then the fee

The payment follows the level-payment formula on the whole amount borrowed, with the annual rate divided by 12, and is the smallest payment in steps of 0.01 whose month-by-month ledger clears the loan. Cash received = amount borrowed − fee. Cost of credit = total interest + fee. The rate including the fee is the monthly rate at which the payments discount to the cash received; it is shown times 12 and as an effective annual rate.

Formula
Payment = P × r ÷ (1 − (1 + r)^−n), with r = annual rate ÷ 12 ÷ 100; cash received = P − fee; cost of credit = total interest + fee
  • Interest for a month = balance at the start of the month × r, rounded to 0.01. Principal repaid = payment − interest.
  • Rate including the fee: the monthly rate i for which the sum of each payment ÷ (1 + i)^k, for k = 1 to n, equals the cash received.
  • Nominal annual rate = i × 12. Effective annual rate = (1 + i)^12 − 1.
  • At a zero rate, payment = P ÷ n, and a fee still produces a rate above zero.

Reconcile 10,000 over 36 months with a 300 fee

Borrow 10,000 at 11% a year for 36 months with a 300 fee taken from the loan. The mathematical payment is 327.387, so the payment is 327.39. You receive 9,700. In month 1 interest is 91.67 and 235.72 reduces the balance. The 36th payment is 327.28. Total interest is 1,785.93 and the cost of credit is 2,085.93. The payments discount to 9,700 at 1.093248% a month, which is 13.1190% times 12 and 13.9373% as an effective annual rate.

The balances come from the same ledger: 7,024.27 after 12 payments and 3,704.18 after 24. With no fee the same payments discount to 10,000 at 11.0000% to four decimal places, so the 300 fee is what adds about 2.12 percentage points.

  1. Enter an amount borrowed of 10000, an annual rate of 11, a term of 36 months and a fee of 300.
  2. Read the payment of 327.39, cash received of 9,700 and a cost of credit of 2,085.93.
  3. Read the annual rate including the fee of 13.1190%, and open the chart's table to follow the balance month by month.

Enter amount, rate, months and fee

Enter the amount borrowed, the annual rate on the reducing balance, the term in whole months and the upfront fee as an amount (0 if none). If the fee is a percentage, work out the amount first: 3% of 10,000 is entered as 300. If the lender adds the fee to the loan, enter the amount borrowed including the fee. Choose a market for number formatting only.

Read the payment, the cash received and the two rates

The monthly payment does not change with the fee, because interest is charged on the amount borrowed. The fee shows up in two places: less cash in hand, and a higher rate once the fee is counted. Compare two offers on the rate including the fee and on the cost of credit, for the same amount received and the same term, and not on the interest rate alone.

The gap between the entered rate and the rate including the fee is in percentage points. The same fee produces a larger gap on a shorter loan, because the fee is spread over fewer months.

One fixed rate and one fee at the start

A fixed nominal annual rate charged at one twelfth each month, equal model months, payments at the end of each month starting one month after the loan is drawn, and one fee taken on the day the loan is drawn. Interest is rounded half up to 0.01 each month. There are no other fees, insurance, taxes, late charges, payment holidays or early repayment.

What the figures leave out

Amounts above 0 up to 1 trillion and fees from 0 to below the amount borrowed, each with at most 2 decimal places; annual rates from 0% to 100%; terms from 1 to 120 whole months. A rate including the fee above 100% a month is reported as not shown. The calculator does not reproduce any country's APR, APRC or comparison-rate rules, and does not estimate what a lender will offer.

Variable rates, fees charged monthly or yearly, insurance, balloon payments, payment holidays and early repayment charges are outside the model. Each can change the payment or the cost.

Compare like with like

Do not compare one loan's interest rate with another loan's APR. Do not enter the fee as a percentage. Do not assume you receive the full amount borrowed when the fee is deducted. Do not read the rate including the fee as the lender's disclosed APR: which charges count, and how the rate is annualised, depend on the country's rules.

How each market describes the rate with fees

In the United States, the CFPB explains that the interest rate is the yearly cost of borrowing without fees and that the APR also reflects fees and other charges, and says to compare APRs with APRs. In the United Kingdom, MoneyHelper describes the APR as the interest rate plus any arrangement fees and notes that lenders must tell you the total amount repayable. In Australia, Moneysmart describes the comparison rate as a single figure that includes the interest rate and most fees, accurate only for the example amount and term given. In Canada, the federal consumer agency says the total cost of a loan includes the amount borrowed, the interest and any other fees. In India, the RBI requires a Key Facts Statement that gives the APR as the annual cost of credit including the interest rate and all other charges. The calculator applies none of these definitions; the market selector changes number formatting only.

Personal loan compared with a plain EMI calculation

The payment arithmetic is the same as for any level-payment loan. A personal loan calculation adds the fee: the cash received, the cost of credit and the rate once the fee is counted. Use the Loan EMI Calculator when there is no fee and you want only the payment schedule, and the Home Loan Calculator when the loan follows from a price and a deposit.

Educational scope

Educational arithmetic for a fixed-rate, level-payment personal loan with one upfront fee. It is not a loan offer, an eligibility or affordability assessment, a regulated APR, APRC or comparison-rate disclosure, or financial advice. A lender's own rounding, day count, fees and conventions will differ; rely on the lender's documents.

Companion calculator

Put the method into practice.

Open Personal Loan Calculator

Frequently asked questions

Is a lower interest rate always the cheaper personal loan?
No. A loan with a lower rate and a larger fee can cost more than one with a higher rate and no fee. Compare the cost of credit and the rate including the fee for the same cash received and the same term.
Does a shorter term make a fee matter more?
Yes. The fee is a fixed amount, so spread over fewer months it adds more to the annual rate. A 1,000 fee on 20,000 at 9.5% adds much more to the rate over 12 months than over 48.
What is the difference between a nominal and an effective annual rate?
A nominal rate is the monthly rate times 12. An effective rate compounds the monthly rate over 12 months, so it is higher whenever the rate is above zero. 1.093248% a month is 13.1190% nominal and 13.9373% effective.
Which fees does the calculator leave out?
Everything except the single upfront fee you enter: late or missed payment charges, early repayment charges, insurance sold with the loan, account fees and taxes on fees. Add any fee charged at the start to the amount you enter.
How much will I actually receive?
The amount borrowed less the fee, when the fee is deducted from the loan. If you need a set amount in hand, you have to borrow more than that amount, and interest is charged on the larger figure.
Why does my lender show a different APR?
Lenders follow their country's disclosure rules, which fix the charges to include, the day count and the way the rate is annualised. They may also date the first payment differently and round in their own way. The lender's disclosure is the figure that counts.

Sources and review

Sources reviewed . Consult current local rules before relying on time-sensitive information.

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