TVM Calculator

What is the Time Value of Money?

The Time Value of Money (TVM) is a fundamental financial concept stating that money available today is worth more than the same amount in the future. This principle exists because money can be invested to earn interest, making a dollar today more valuable than a dollar received later.

TVM calculations are essential for making informed financial decisions about loans, investments, retirement planning, and any scenario where money changes hands over time. Understanding TVM helps you compare financial options and determine the true cost or value of money across different time periods.

The 5 TVM Variables

N - Number of Periods

The total number of payment periods in the loan or investment. For a 30-year mortgage with monthly payments, N = 360 (30 years × 12 months). This is the time horizon over which cash flows occur.

I/Y - Interest Rate per Year

The annual interest rate as a percentage. The calculator automatically converts this to a periodic rate based on your payment frequency (P/Y). For example, 6% annual with monthly payments becomes 0.5% per month.

PV - Present Value

The current lump sum value. For loans, this is the amount borrowed (positive because you receive it). For investments, this is your initial deposit (negative because you pay it out). PV represents money at time zero.

PMT - Payment

The periodic payment amount that occurs each period. For loans, payments are negative (you pay them). For receiving an annuity, payments are positive (you receive them). PMT is the recurring cash flow.

FV - Future Value

The value at the end of all periods. For fully amortizing loans, FV is typically 0 (loan is paid off). For savings goals, FV is your target amount (positive because you'll receive it). FV represents money at time N.

Payment Timing: END vs BGN Mode

END Mode (Ordinary Annuity): Payments occur at the end of each period. This is the default for most loans and investments. Your first payment is due at the end of period 1.

BGN Mode (Annuity Due): Payments occur at the beginning of each period. Common for rent, lease payments, and some insurance premiums. Your first payment is due immediately (at time 0).

BGN mode typically results in slightly lower payments for loans because each payment has one additional period to earn interest before the end.

How to Use This Calculator

1. Select what to solve for - Click the variable you want to calculate (N, I/Y, PV, PMT, or FV)
2. Enter the known values - Fill in the four variables you know
3. Set payment frequency - Choose how often payments occur (monthly is most common)
4. Choose END or BGN mode - Select when payments occur within each period
5. Review results - The calculator instantly shows your answer plus totals and effective rate
6. Explore amortization - For loans, expand the schedule to see payment-by-payment breakdown

Common TVM Scenarios

Mortgage/Loan Payment Calculation

To find your monthly payment: Set PV as the loan amount (positive), FV = 0, enter I/Y and N, solve for PMT. The result is negative, indicating cash you pay out each month.

Retirement Savings Goal

To find how much you need to save monthly: Set FV as your goal (positive), PV = 0 or your current savings (negative), enter I/Y and N, solve for PMT. The negative result shows your required monthly contribution.

Investment Growth

To find what an investment will grow to: Set PV as your initial investment (negative), enter I/Y and N, PMT for any additional contributions, solve for FV. The positive result is your ending balance.

Loan Payoff Time

To find when a loan will be paid off: Set PV as balance owed (positive), PMT as your payment (negative), FV = 0, I/Y as rate, solve for N. The result tells you how many payments remain.

TVM Formulas

The fundamental TVM equation relates all five variables:

Where i is the periodic interest rate (I/Y ÷ P/Y ÷ 100) and n is the total number of periods (N).

For annuity due (BGN mode), the PMT term is multiplied by (1+i) to account for payments occurring at the beginning of each period.