TVM Finance, Present Value & Effective APR Calculator

Compute Future Value, Present Value, Required Monthly Payment, and Newton-Raphson Effective APR with upfront loan fees.

Future Value (FV)
USD 106,180.72
N = 120 mos • Nominal I/Y = 7.5% • Effective APR (with USD 1,500.00 fees) = 8.927%
Future Value (FV) USD 106,180.72
Present Value (PV) USD 60,783.70
Required Monthly PMT USD 124.76
Effective APR (Newton Solver) 8.927%
Inputs
Amounts are treated in the selected currency; no foreign-exchange conversion is applied.
All four metrics are computed simultaneously below.
months
Total compounding/payment months (e.g. 120 = 10 years).
% / yr
Annual nominal interest or discount rate.
USD ($)
Starting capital or loan principal.
USD / mo
Monthly cashflow addition.
USD ($)
Target future amount for PV discounting or PMT solver.
USD ($)
Origination fees financed into the loan for APR calculation.
Results & Graph
Future Value (FV)
USD 106,180.72
N = 120 mos • Nominal I/Y = 7.5% • Effective APR (with USD 1,500.00 fees) = 8.927%
Future Value (FV)
USD 106,180.72
Present Value (PV)
USD 60,783.70
Required Monthly PMT
USD 124.76
Effective APR (Newton Solver)
8.927%

Time Value of Money Component Breakdown (USD)

Starting Present Value vs. Cumulative Periodic Payments vs. Compounded Interest
Graph 1 • Compound Cashflow Trajectory (0 to N Periods) Solid = Compounded Future Value; Dashed = Principal + PMT additions
0 57.3k 114.7k Mo 0: 25,000 25.0k Mo 0 Mo 30: 40,003 40.0k Mo 30 Mo 60: 58,090 58.1k Mo 60 Mo 90: 79,895 79.9k Mo 90 Mo 120: 106,181 106.2k Mo 120
Graph 2 • Present Value vs. Periodic Payments vs. Compound Interest Share of ending Future Value
FUTURE VALUE USD 106,200.00 Starting Principal (PV) 25.0k (23.5%) Cumulative Payments (N × PMT) 36.0k (33.9%) Compounded Interest 45.2k (42.6%)
Graph 3 • Stated Rate vs. Effective APY vs. Fee-Adjusted APR Shows how upfront origination fees raise effective borrowing cost
Stated Nominal Interest Rate (I/Y) 7.500% p.a. Effective Annual Percentage Yield (EAR) 7.763% APY Regulation Z Effective Loan APR (Including Fees) 8.610% APR
Summary: Future value is USD 106,180.72, present value is USD 60,783.70, and effective APR is 8.927%.
Summary: Across N = 120 monthly periods at 7.5% p.a., a USD 25,000.00 starting balance plus USD 300.00/month grows to USD 106,180.72. Discounting back to today yields a Present Value of USD 60,783.70. On a loan of USD 25,000.00 with USD 1,500.00 in upfront origination fees, the true effective APR solved via Newton-Raphson iteration is 8.927%.
⚡ Send result to: Compound Interest →Loan / EMI →Mortgage →
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Formula & Mathematical Methodology: TVM Cashflow Identity & Newton-Raphson Effective APR

FV = PV(1 + r)n + PMT · [(1 + r)n − 1r]
PV − Fees = PMT · [1 − (1 + rAPR)−nrAPR]
FV = PV(1+r)^n + PMT[((1+r)^n − 1)/r]; NetLoan = PV − Fees = PMT[(1 − (1+r_apr)^(−n))/r_apr]
  • N, r: Monthly periods and periodic monthly rate (I/Y ÷ 12)
  • rapr: Monthly internal rate of return solved via Newton-Raphson iteration

Rounding: Currency rounds to 2 decimal places; APR rounds to 3 decimal places.

Worked Example: $25,000 PV + $300/Mo for 120 Months at 7.5% (Plus $1,500 Loan Fee APR Check)

Evaluate FV, PV, and effective APR across 120 months at 7.5%.

  1. Future Value of $25k + $300/mo over 120 months = $106,073.40.
  2. If $25,000 is a loan with $1,500 in upfront fees (net proceeds $23,500), Newton-Raphson iteration solves the effective APR as 8.887%.
Result: FV is $106,073.40 and effective APR with $1,500 fees is 8.887%.

Frequently Asked Questions

Why is the APR higher than the stated nominal interest rate on a loan?

Truth in Lending (Regulation Z) requires APR to amortize upfront origination fees and discount points over the life of the loan, reducing your net cash received while keeping your monthly payment based on the gross principal.

Finance & Investing · Time Value of Money & Credit Solvers

TVM Finance, Present Value & Effective APR Calculator: inputs, method, and how to read the result

Compute Future Value, Present Value, Required Monthly Payment, and Newton-Raphson Effective APR with upfront loan fees.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Display Currency: Amounts are treated in the selected currency; no foreign-exchange conversion is applied.
  • Primary Solver Target: All four metrics are computed simultaneously below.
  • Number of Monthly Periods (N): Total compounding/payment months (e.g. 120 = 10 years).
  • Nominal Annual Rate (I/Y): Annual nominal interest or discount rate.

What the calculation includes

With the default values shown, Future Value (FV) is USD 106,180.72. The calculation follows TVM Cashflow Identity & Newton-Raphson Effective APR; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Primary Solver Target from Solve for Future Value (FV) to Solve for Present Value (PV) changes Future Value (FV) (USD 106,180.72) to Present Value (PV of FV + Cashflows) (USD 60,783.70). This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Ordinary annuity end-of-period cashflow convention.
  • Assumes equal monthly intervals; for irregular dates use CAGR/IRR.

Scope: Global Check the assumptions and limitations against your situation before relying on the estimate.

More in Finance & Investing: Compound Interest Calculator, Loan & EMI Calculator, Mortgage Calculator.