Time Value of Money Calculator – PV, FV, Payment and Periods
The Time Value of Money Calculator helps you solve the core equations behind most financial decisions. Whether you are saving for a goal, evaluating an investment, or analyzing a loan, time value of money formulas connect four key variables: present value, future value, interest rate and number of periods. When recurring payments are involved, annuity formulas extend the same framework.
Instead of working through complex equations by hand, this calculator lets you plug in your known values and solve for the unknown. You can calculate future value from present value and payments, find the present value of future cash flows, determine the periodic payment needed to reach a target, or estimate how long it will take to reach a financial goal at a given interest rate.
How the Time Value of Money Calculator Works
The calculator is organized into four modes:
- Future Value (FV): Calculates how much your money will grow to, including optional regular payments.
- Present Value (PV): Discounts future lump sums and payments back to today’s value.
- Periodic Payment (PMT): Finds the payment needed to achieve a target future value or pay down a present value.
- Number of Periods (N): Estimates how many periods it takes for a present value to reach a given future value.
You can specify the annual interest rate, number of years and payments per year. The tool then converts everything into per-period values for accurate compounding.
Core Time Value of Money Concepts
The time value of money is built on the idea that a sum of money today can be invested to earn interest, so it will be worth more in the future. Likewise, a future cash amount must be discounted back to find its value today. When payments repeat over time, such as monthly deposits or loan instalments, annuity formulas are used.
Future Value of a Lump Sum
Where PV is present value, i is interest rate per period and n is number of periods. For example, if you invest $10,000 at 6% compounded annually for 10 years, there are 10 periods at 6% per period.
Future Value of an Annuity
If payments occur at the beginning of each period (annuity due), the factor is multiplied by (1 + i). The calculator uses this logic based on your payment timing selection.
Present Value of a Future Amount
Present Value of an Annuity
For payments at the beginning of each period, the annuity factor is again multiplied by (1 + i).
Mode 1: Future Value (FV)
The Future Value mode calculates how much a combination of a starting amount and recurring payments will be worth after a certain time at a given interest rate. This is useful for savings plans, investment projections and goal-based planning.
Inputs include present value, annual interest rate, years, payments per year, periodic payment and payment timing. The calculator converts the annual rate to a per-period rate and multiplies years by payments per year to find the total number of periods.
The result is broken into three parts: future value of the lump sum, future value of all payments and the total future value. This breakdown helps you see how much growth comes from initial capital versus ongoing contributions.
Mode 2: Present Value (PV)
The Present Value mode answers the question: “What is this future cash flow worth today?” It works for a single future lump sum, for a series of payments, or for a combination of both. This is a key concept in valuing investments, retirement income streams and loan offers.
You enter future value, interest rate, years, payments per year, periodic payment and payment timing. The calculator discounts the future lump sum and each payment back to the present using the same per-period rate and number of periods. The results show present value of the lump sum, present value of the annuity and total present value.
Mode 3: Periodic Payment (PMT)
The Payment mode solves for the recurring payment that satisfies your constraints. You can enter a present value (such as an existing balance), a desired future value (such as a savings goal), an interest rate, number of years and payments per year. The calculator solves the payment needed per period.
For example, you might want to know how much to save monthly to reach a target amount at retirement, or what loan payment will pay off a balance in a certain number of years. The calculator reports the required payment, the total number of payments, the total amount paid and the total interest portion.
Mode 4: Number of Periods (N)
The Number of Periods mode estimates how long it takes for a present value to grow into a future value at a certain interest rate, assuming there are no recurring payments. It is helpful when you have a starting amount, a target and an expected rate of return, and want to know the time required.
The calculator outputs total periods and equivalent years. You can adjust the interest rate or target amount and see how that changes the required time.
Choosing Payments per Year and Timing
Financial products often compound and make payments more frequently than once a year. For example, loans may require monthly payments, and investment accounts may be funded monthly or quarterly. Payments per year describes this frequency. If you select 12, the annual rate is divided by 12 and years are multiplied by 12 to determine per-period rate and periods.
Payment timing controls whether payments occur at the end or beginning of each period. End-of-period payments represent ordinary annuities, typical for most loans. Beginning-of-period payments represent annuities due, such as rent or some savings plans that deposit at the start of a month.
Examples of Time Value of Money Calculations
Example 1: Future Value of a Lump Sum and Monthly Savings
You invest $5,000 today and add $200 every month for 15 years at an annual rate of 7%, compounded monthly. The Future Value mode treats the 7% as 7 ÷ 12 per month and multiplies 15 years by 12, then computes the future value of the lump sum and all monthly payments to show your total amount.
Example 2: Present Value of a Future Goal
You want $100,000 in 12 years and expect a 5% annual return. Using the Present Value mode with no payments, the calculator discounts $100,000 back 12 years at 5% to show how much you would need to invest today as a lump sum.
Example 3: Payment Needed to Reach a Target
You start with no savings, want $250,000 in 25 years, expect a 6% annual return and will invest monthly. The Payment mode solves the required monthly contribution, then shows how much you will contribute in total and how much of the final amount comes from investment growth.
Example 4: Time Needed to Double Money
You invest $10,000 at 7% compounded annually and want to know when it will reach $20,000. The Number of Periods mode calculates the number of years required, using the logarithmic formula for growth.
How to Use This Tool Effectively
- Decide which variable you want to solve for: FV, PV, payment or periods.
- Enter the known values, including interest rate, time and payment frequency.
- Choose payment timing that matches your scenario.
- Use different modes to cross-check: for example, use the payment result in the future value mode.
- Experiment with different interest rates and durations to understand how sensitive your plan is to changes in return or time.
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Time Value of Money Calculator FAQs
Frequently Asked Questions About Time Value of Money
Quick answers about present value, future value, payments and periods.
Present value is today’s value of a cash amount. Future value is what that cash will grow to after compounding at a given interest rate.
You can use an expected return for investments, a quoted rate for a loan or a conservative assumption for long-term planning. Results depend on this choice.
Yes. Payments per year also control the compounding frequency. For example, 12 means monthly, 4 means quarterly and 1 means annual compounding.
Ordinary annuities pay at the end of each period, while annuities due pay at the beginning. The calculator supports both via the payment timing setting.
Yes. The same time value of money formulas apply to savings plans, investment projections, mortgages, car loans and other instalment products.