What is the time value of money (TVM)?

The time value of money states that a dollar today is worth more than a dollar in the future, because money available now can be invested to earn returns. TVM is the foundation of all financial calculations including loans, investments, and present/future value analysis.

What is the difference between PV and FV?

PV (Present Value) is what a future amount of money is worth today, after discounting for time and interest. FV (Future Value) is what a current amount of money will be worth in the future after earning interest. FV = PV × (1 + r)^n.

What is PMT in finance?

PMT (Payment) is the regular periodic payment in a financial calculation — such as monthly loan payments, mortgage installments, or regular investment contributions. In loan calculations, PMT is negative (cash out); in savings, it can be positive (cash in).

What is I/Y in a financial calculator?

I/Y is the periodic interest rate (Interest per Year or per Period). It represents the rate at which money grows or costs per compounding period. For monthly calculations, divide the annual rate by 12 to get the monthly rate.

What is the difference between beginning and end mode in TVM?

In End mode (ordinary annuity), payments occur at the END of each period — standard for most loans. In Beginning mode (annuity due), payments occur at the START of each period — common for leases and some savings plans. Beginning mode results in slightly higher FV and lower PV than End mode because money has one extra period to earn interest.

How do I calculate monthly loan payments?

Set N = total months (years × 12), I/Y = annual rate ÷ 12, PV = loan amount (positive), FV = 0, and solve for PMT. The result will be negative, representing cash outflow. For a $200,000 loan at 6% for 30 years: N=360, I/Y=0.5%, PV=200,000, FV=0, PMT = -$1,199.10.

Finance Calculator – PV, FV, PMT, Rate & N | Time Value of Money | PrimeCalculator

🧮 TVM Finance Calculator

Finance Calculator — PV, FV, PMT, Rate & N

Solve for any Time Value of Money variable — Present Value, Future Value, Payment, Interest Rate, or Number of Periods. Includes period schedule and formula display.

🔢 5 TVM Variables

📋 Period Schedule

📐 Formula Display

🔄 Begin/End Mode

🧮

Finance / TVM Calculator

Time Value of Money — Solve for any variable

Solve For:

TVM Variables

N — Number of Periods

per

I/Y — Interest Rate (per period)

PV — Present Value

FV — Future Value

PMT — Payment (per period)

Settings

Payment Timing

End (Ordinary) Beginning (Due)

Periods Per Year (for I/Y interpretation)

Present Value

Future Value

Payment (PMT)

Total Interest

Formula Used

PMT = PV × [r(1+r)^n] / [(1+r)^n − 1]

where r = I/Y per period, n = number of periods

📊 Balance Over Time

📋 Period-by-Period Schedule

Period	Opening Balance (PV)	Payment	Interest	Closing Balance
Enter values above to see schedule

💡 TVM Quick Reference

📐For a loan: enter PV = loan amount (positive), FV = 0, solve for PMT (will be negative)

📈For savings: enter PV = starting amount, PMT = regular deposit, solve for FV

🔄Beginning mode payments earn one extra period of interest vs End mode

💡I/Y is the rate PER PERIOD — for monthly, enter monthly rate (annual ÷ 12)

🔢N is total periods — for a 30-year monthly loan: N = 30 × 12 = 360

⚠️Cash outflows (loan payments) are negative; cash inflows (received money) are positive

The 5 TVM Variables Explained

Every financial calculation — loans, investments, savings, mortgages — is built on five Time Value of Money (TVM) variables. Give the calculator any four, and it solves for the fifth.

Variable	Full Name	What It Means	Example
N	Number of Periods	Total payment or compounding periods	360 for a 30-year monthly loan
I/Y	Interest per Period	Rate per period (annual rate ÷ periods/year)	0.5% per month = 6% APR ÷ 12
PV	Present Value	Value of money today (or loan amount)	$200,000 mortgage
FV	Future Value	Value at end of last period	$0 for a fully repaid loan; $500,000 retirement goal
PMT	Payment	Regular periodic payment or contribution	-$1,199/month (negative = outflow)

Common Finance Calculator Scenarios

🏠 Mortgage Payment (Solve for PMT)

N = 360, I/Y = 0.5% (6% ÷ 12), PV = $200,000, FV = 0 → PMT = −$1,199.10/month. Total paid over 30 years: $431,676. Total interest: $231,676.

💰 Savings Goal (Solve for FV)

N = 240, I/Y = 0.583% (7% ÷ 12), PV = $10,000, PMT = $500 → FV = $326,617 after 20 years.

📈 Required Monthly Saving (Solve for PMT)

N = 360, I/Y = 0.583%, PV = $0, FV = $1,000,000 → PMT = $820.03/month to reach $1M in 30 years.

🔢 How Long to Pay Off a Loan (Solve for N)

I/Y = 1.5% (18% ÷ 12), PV = $5,000 credit card balance, FV = 0, PMT = −$150 → N = 47 months (nearly 4 years) and $2,024 in interest.

Beginning vs End Mode (Ordinary vs Due Annuity)

End mode (Ordinary Annuity): Payments occur at the END of each period. This is standard for most loans — your first mortgage payment is due one month after closing. Interest accrues first, then you pay.

Beginning mode (Annuity Due): Payments occur at the START of each period. Used for leases, some savings plans, and insurance premiums. Because you pay upfront, slightly less total interest accrues — each payment has one extra period to reduce the balance or earn interest.

Frequently Asked Questions

TVM states that a dollar today is worth more than a dollar in the future because money available now can be invested to earn interest. This concept underlies every financial calculation — loans, investments, mortgages, and retirement planning. TVM formulas connect PV, FV, PMT, rate, and time periods to quantify this relationship.

I/Y stands for Interest per Year (or more precisely, interest per period). On most financial calculators, I/Y is entered as the annual percentage rate, and the calculator divides by periods per year. In our calculator, enter I/Y as the RATE PER PERIOD — so for a 6% annual loan with monthly payments, enter 0.5 (6 ÷ 12 = 0.5% per month).

In TVM sign conventions, cash outflows are negative and cash inflows are positive. When you take a loan, PV (money you receive) is positive. Your monthly payments are cash going OUT of your pocket — so PMT is negative. Conversely, if you're a bank collecting loan payments, PMT would be positive. Always be consistent: if PV is positive, PMT should be negative for a loan.

For an ordinary annuity (End mode): PMT = PV × [r(1+r)^n] / [(1+r)^n − 1], where r = interest rate per period and n = number of periods. For annuity due (Beginning mode): divide by (1+r). For example, a $200,000 loan at 6% APR monthly for 30 years: PMT = 200,000 × [0.005(1.005)^360] / [(1.005)^360 − 1] = $1,199.10.

PV (Present Value) is today's value of a future cash flow or series of payments, discounted at the given interest rate. FV (Future Value) is the value of a current sum at a future date after earning interest. For a loan: PV = loan amount (money received now), FV = 0 (fully repaid). For savings: PV = starting balance, FV = your future goal.

Enter the four known TVM variables (N, I/Y, PV, FV, PMT) and select the fifth to solve for. For I/Y, enter the PERIODIC rate (not annual) — e.g., 0.5 for 6% annual with monthly periods. Choose End/Beginning mode at the bottom. The result and period schedule match what a financial calculator would produce. Note: our I/Y input is per period, while the BA II Plus uses annual rate — divide by P/Y first.