Skip to content
TrueScalers

Loan calculator

A loan calculator finds the level monthly payment on a fixed-rate loan using M = P × [r(1+r)ⁿ] ÷ [(1+r)ⁿ − 1], where P is the amount borrowed, r is the annual rate divided by 12, and n is the number of monthly payments. A $20,000 loan at 9.5% over 5 years costs $420.04 per month and $5,202 in total interest.

$
%
years
$
Calculated in your browser — nothing is uploaded.

Result

Monthly payment

$420.04

M = P × [r(1+r)ⁿ] ÷ [(1+r)ⁿ − 1]

Total interest
$5,202.23
Total repaid
$25,202.23
Number of payments
60

A $20,000 loan at 9.50% over 5 years costs $420.04 per month, with $5,202.23 of total interest and $25,202.23 repaid across 60 payments.

How to use the loan calculator

  1. 01

    Enter the loan amount

    Type the principal you intend to borrow. Exclude any origination fee deducted at disbursement, and add it separately if it is rolled into the balance.

  2. 02

    Enter the annual rate

    Type the annual percentage rate the lender quoted. Use the APR rather than the nominal rate when fees are included in the quote.

  3. 03

    Enter the term

    Type the repayment period in years. Quarter-year steps allow terms such as 3 years 6 months.

  4. 04

    Optionally add an extra payment

    Enter a fixed amount to overpay each month. The calculator then shows the shortened payoff period and the interest saved.

  5. 05

    Read the totals

    The result strip shows the monthly payment, and the rows beneath show total interest, total repaid and the number of payments.

The formula

M = P × [r(1 + r)ⁿ] ÷ [(1 + r)ⁿ − 1]
M
The level monthly payment.
P
The principal — the amount borrowed at the start.
r
The monthly interest rate: the annual percentage rate divided by 100, then by 12.
n
The total number of monthly payments: the term in years multiplied by 12.

This is the standard amortization formula for any fixed-rate, level-payment loan: personal loans, student loans, auto finance and mortgages all use it. It assumes interest accrues on the declining balance, which is how virtually all consumer instalment credit works in the United States, the United Kingdom and the European Union.

Worked example

Loan amount
$20,000
Annual rate
9.5%
Term
5 years
Extra monthly payment
$0
Result
$420.04 per month

The monthly rate r is 9.5 ÷ 100 ÷ 12 = 0.00791667, and n is 5 × 12 = 60 payments. Raising (1 + r) to the 60th power gives 1.60586. Substituting into the formula: M = 20,000 × (0.00791667 × 1.60586) ÷ (1.60586 − 1) = 20,000 × 0.01271305 ÷ 0.60586 = $420.04. Across all 60 payments the borrower repays $25,202, of which $5,202 is interest — 26% of the amount borrowed.

Frequently asked questions

How is a loan payment calculated?

A fixed-rate loan payment is calculated with the amortization formula M = P × [r(1+r)ⁿ] ÷ [(1+r)ⁿ − 1]. The result is a level payment that fully repays both principal and interest by the final instalment. Early payments are mostly interest because interest accrues on a large outstanding balance; later payments are mostly principal.

What is the difference between interest rate and APR?

The interest rate is the cost of borrowing the principal alone. The annual percentage rate additionally includes lender fees, points and certain closing costs, expressed as a yearly rate. US Regulation Z requires lenders to disclose APR precisely so that offers with different fee structures can be compared on one number.

Does paying a loan off early save money?

Almost always, because interest accrues on the outstanding balance each month. Repaying early reduces the balance sooner and every subsequent interest charge with it. The exception is a loan with a prepayment penalty or one using the Rule of 78s, an interest-front-loading method now restricted for most consumer loans in the United States.

What is amortization?

Amortization is the process of repaying a debt through scheduled level payments that cover both interest and principal. Each payment first covers the interest accrued that period, and the remainder reduces the balance. Because the balance falls, the interest portion shrinks every period and the principal portion grows by the same amount.

How much does a longer loan term actually cost?

A longer term lowers the monthly payment but raises total interest. A $20,000 loan at 9.5% costs $420.04 a month over 5 years with $5,202 of interest, or $632.07 a month over 3 years with $2,754 of interest. The three-year term costs $212 more each month and saves $2,448 overall.

What is a simple interest loan?

A simple interest loan charges interest on the outstanding principal only, never on accumulated interest. Most consumer instalment loans work this way, which is why paying a few days early reduces the interest charged. Compound interest, by contrast, charges interest on previously accrued interest and is the norm for credit-card balances.

Sources

Last reviewed: · Formula and sources verified by Syed Aqeel Ahmad Gillani. See the methodology for how every calculation is derived.

Related tools