Finance Calculator for Loans and Investments
Finance Calculator
Time Value of Money Calculator
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The finance calculator is a general-purpose tool for solving time-value-of-money problems. Given any four of the five variables (present value, future value, payment, rate, number of periods), it solves for the fifth. This is the same calculation underlying mortgages, investments, annuities, leases, and virtually all loan and savings problems.
Time Value of Money
The core principle of finance is that a dollar today is worth more than a dollar in the future because money can be invested to earn returns. All financial calculations involving cash flows over time use this concept. The five TVM variables are interrelated, and knowing four allows you to solve for the fifth.
| Variable | Abbreviation | Meaning |
|---|---|---|
| Present Value | PV | Current value of future cash flows |
| Future Value | FV | Value at a specified future date |
| Payment | PMT | Regular periodic cash flow |
| Interest Rate | I/Y or r | Rate per period |
| Number of Periods | N | Total number of time periods |
Common Finance Calculations
The same TVM framework solves for different unknowns depending on what you know.
FV = PV × (1+r)^n (no payments) PV = FV / (1+r)^n (reverse) PMT = [PV × r] / [1 - (1+r)^-n] (loan payment) N = ln(FV/PV) / ln(1+r) (time to goal) R: solve numerically
All variables must use consistent time periods (monthly rate with monthly periods, etc.).
Frequently Asked Questions
What is the difference between present value and future value?⌄
Present value is what a future amount is worth today, discounted at a given rate. Future value is what today's money will grow to at a given rate over time. They are the same concept viewed from opposite directions: PV × (1+r)^n = FV. If you invest $1,000 today at 5% for 10 years, FV = $1,629. The PV of $1,629 in 10 years at 5% is $1,000.
How do I solve for the interest rate?⌄
Enter PV, FV, PMT (if applicable), and N. The calculator will solve for the rate using iterative numerical methods. This is useful for finding the implicit return on an investment, verifying a loan rate, or determining the yield on a series of cash flows.
What is the Rule of 72?⌄
The Rule of 72 is a quick approximation: divide 72 by the annual interest rate to find the approximate number of years to double your money. At 6%, money doubles in 72/6 = 12 years. At 9%, in 72/9 = 8 years. It is accurate within a few percent for rates between 2% and 20%.
What is the difference between ordinary annuity and annuity due in TVM?⌄
Ordinary annuity (END mode): payments occur at the end of each period. Annuity due (BEGIN mode): payments occur at the beginning. Annuity due values are slightly higher because each payment has one extra period to compound. Financial calculators typically have a BEGIN/END setting for this. Most loan calculations use END mode.