Implied Interest Rate Calculator

This calculator answers the question: what percent is my loan’s interest really? Enter the loan principal, installment per period, and term, and the solver finds the single interest rate that makes the present value of all installments exactly equal the principal. Example: a loan of Rp500,000,000 with installments of Rp10,138,197.14 over 60 months gives an implied interest rate of 8.000000% per year (nominal, monthly compounding). This is the same figure the RATE function in spreadsheets computes.

There is no closed-form formula to invert the installment formula, so the calculator uses the bisection method: because the installment rises monotonically as the interest rate rises, the solution is guaranteed to be bracketed between two bounds. The solver starts from a 0% to 100% per-period range, takes the midpoint, discards the wrong half of the range, and repeats. After about 40 iterations, the range narrows to below 0.0000000001% and the result stabilizes. All iterations are shown on the results panel so you can verify the convergence yourself.

Both measure the true cost of a loan, but with different math. The Effective Interest Rate Calculator uses a simple total-cost method: total interest plus fees divided by net funds received, divided by years, plus the constant-ratio formula for add-on or flat loans. This calculator uses a pure actuarial solver: it needs no fee data at all, only the actual installments you pay. Use the effective interest rate when you want to include origination and administration fees; use this calculator when you only know the installment and want to know the rate.

The Equivalent Interest Rate Calculator answers a conversion question: what percent is 12% nominal monthly compounding equal to under quarterly compounding? It does not find the size of the interest rate; it translates an already-known rate across frequencies. This calculator performs the earlier step: finding the size of the rate itself from your installment. Once the implied rate is found, the EAR tab here uses the same equivalence logic to convert it to EAR.

The APR Calculator starts from the opposite side: you enter the nominal interest rate plus upfront fees, it builds an amortization schedule, then solves the actuarial rate against the net funds received. This calculator starts from the actual installment: no need to know the nominal rate or its details — just principal, installment, and term. Both results will be similar when the installments are consistent, but the paths differ.

This estimate assumes fixed installments each period and no upfront fees. Loans with floating rates, late penalties, or origination fees deducted from disbursement are not modeled, so the actual rate may differ. Mathematically, a solution exists only when the installment is at least the principal divided by the term; a smaller installment has no nonnegative interest-rate solution. The result is a mathematical estimate for comparison purposes, not financial advice; for loan decisions, consult a professional financial planner.

A nominal interest rate of 8% per year with monthly compounding actually yields 8.299951% per year when measured as the effective annual rate (EAR), because the current month’s interest earns interest in the following month. EAR is the only fair figure for comparing two offers with different compounding frequencies. That is why every result in this calculator always shows nominal and EAR side by side.