Solve for any of the 5 key financial Time Value of Money (TVM) variables: Future Value (FV), Present Value (PV), Periodic Payment (PMT), Interest Rate (I/Y), or Number of Periods (N).
Value changes over time
Amortization & Balance Schedule
Below is the step-by-step breakdown of how the balance accumulates/depletes period-by-period.
| Period | Start Balance | Payment | Interest | End Balance |
|---|---|---|---|---|
| 1 | $20,000.00 | $2,000.00 | $1,200.00 | $19,200.00 |
| 2 | $19,200.00 | $2,000.00 | $1,152.00 | $18,352.00 |
| 3 | $18,352.00 | $2,000.00 | $1,101.12 | $17,453.12 |
| 4 | $17,453.12 | $2,000.00 | $1,047.19 | $16,500.31 |
| 5 | $16,500.31 | $2,000.00 | $990.02 | $15,490.33 |
| 6 | $15,490.33 | $2,000.00 | $929.42 | $14,419.75 |
| 7 | $14,419.75 | $2,000.00 | $865.18 | $13,284.93 |
| 8 | $13,284.93 | $2,000.00 | $797.10 | $12,082.03 |
| 9 | $12,082.03 | $2,000.00 | $724.92 | $10,806.95 |
| 10 | $10,806.95 | $2,000.00 | $648.42 | $9,455.36 |
The Time Value of Money (TVM)
Suppose someone owes you $500. Would you rather have this money repaid to you right away in one payment or spread out over a year in four installment payments? How would you feel if you had to wait to get the full payment instead of getting it all at once? Wouldn't you feel that the delay in the payment cost you something?
According to a concept that economists call the "time value of money," you will probably want all the money right away because it can immediately be deployed for many different uses: spent on the lavish dream vacation, invested to earn interest, or used to pay off all or part of a loan. The "time value of money" refers to the fact that a dollar in hand today is worth more than a dollar promised at some future time.
This is the basis of the concept of interest payments; a good example is when money is deposited in a savings account, small dividends are received for leaving the money with the bank; the financial institution pays a small price for having that money at hand. This is also why the bank will pay more for keeping the money in long and for committing it there for fixed periods.
This increased value in money at the end of a period of collecting interest is called future value in finance. Here is how it works.
Future Value Example
Suppose $100 (PV) is invested in a savings account that pays 10% interest (I/Y) per year. How much will there be in one year? The answer is $110 (FV). This $110 is equal to the original principal of $100 plus $10 in interest. $110 is the future value of $100 invested for one year at 10%, meaning that $100 today is worth $110 in one year, given that the interest rate is 10%.
PMT (Periodic Payment)
PMT or periodic payment is an inflow or outflow amount that occurs at each period of a financial stream. Take, for instance, a rental property that brings in rental income of $1,000 per month, a recurring cash flow. Investors may wonder what the cash flow of $1,000 per month for 10 years is worth. Otherwise, they have no conclusive evidence that suggests they should invest so much money into a rental property.
The Importance of the Finance Calculator
In essence, our Finance Calculator is the foundation for most of our Financial Calculators. It helps to think of it as an equivalent to the steam engine that was eventually used to power a wide variety of things such as the steamboat, railway locomotives, factories, and road vehicles. There can be no Mortgage Calculator, or Credit Card Calculator, or Auto Loan Calculator without the concept of the time value of money as explained by the Finance Calculator.
How it Works & Formula
The basic formula ties all 5 elements together using compounding period interest. When rate is 0%, it simplifies to: PV + (PMT * N) + FV = 0.
Practical Examples
A project costing $50,000 that returns $20,000 annually for 3 years at a discount rate of 10% has an NPV of $47,715 - $50,000 = -$2,285.
Frequently Asked Questions
What do PV, FV, PMT, I/Y, and N represent?
PV is Present Value (starting amount), FV is Future Value (ending target), PMT is the periodic payment, I/Y is the annual Interest Rate (%), and N is the total number of periods.
Why do some values need to be negative?
This calculator follows standard accounting and financial cashflow conventions. Outflows (money you invest, pay, or save) are represented as negative numbers (-), while inflows (loans received or withdrawals) are positive (+).
What are P/Y and C/Y?
P/Y stands for Payments per Year, and C/Y stands for Compounding periods per Year. For instance, if you make monthly payments but interest compounds semi-annually, P/Y would be 12 and C/Y would be 2.