Compound Interest and Time Value of Money Calculator
Inputs & Results
Methodology: client-side calculations use standard time value of money formulas for discrete compounding, annuities, APR, and EAR.
Educational estimates only. Taxes, fees, inflation, and variable rates are excluded unless you adjust the inputs manually. Last reviewed: June 9, 2026. Content by Starlight Robotics.
Initial balance today.
Enter the yearly nominal rate, not the monthly rate.
Whole years before any extra months.
Use 0 if the term is an exact number of years.
How often the annual rate is credited.
Optional amount added each payment period. Use 0 for lump sum only.
How often regular deposits are made.
Start-of-period deposits earn one extra payment period of interest.
Advanced mode: use the rate for one compounding period, not the annual APR.
Monthly for 10 years means 120 periods.
Tip: Enter rates as % per period (e.g., type 1 for 1% each month).
Match this rate to the payment period.
Count payment periods, not calendar years.
Periodic rate for the selected cash-flow interval.
Use the same period unit as the rate and payments.
Annual = 1, quarterly = 4, monthly = 12, daily = 365.
Calculation Guide
Use the first tab for everyday compound-interest questions: starting balance, annual rate, time, compounding frequency, and optional deposits. Use the advanced tabs when you already know the periodic rate \(i\) and periods \(n\).
Annual APR to periodic rate: \(i=r/m\). Future value: \(FV=PV(1+i)^n\).
Effective annual rate: \(EAR=(1+r/m)^m-1\). Continuous comparison: \(FV=PV e^{rt}\).
- Annual rate: the nominal yearly rate or APR entered as a percent.
- Compounding frequency: how often interest is credited each year.
- Payment frequency: how often regular deposits or payments occur.
- Payment timing: end-of-period is ordinary annuity; start-of-period is annuity due.
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Compound Interest and Time Value of Money Guide
Discrete compounding means interest is applied at fixed intervals. A yearly APR can be split into annual, quarterly, monthly, weekly, or daily periods. The calculator converts annual inputs into the matching periodic rate, then reports future value, present value, interest, payment totals, a schedule, and calculation steps.
Formula Table
| Need | Formula | Use when |
|---|---|---|
| Future value | \(FV=PV(1+i)^n\) | Grow a present amount forward. |
| Present value | \(PV=\dfrac{FV}{(1+i)^n}\) | Discount a future amount to today. |
| Solve for rate | \(i=\left(\dfrac{FV}{PV}\right)^{1/n}-1\) | Find the periodic return for a lump sum. |
| Solve for time | \(n=\dfrac{\ln(FV/PV)}{\ln(1+i)}\) | Find periods needed for a lump sum target. |
| Ordinary annuity FV | \(FV=A\dfrac{(1+i)^n-1}{i}\) | Payments at the end of each period. |
| Ordinary annuity PV | \(PV=A\dfrac{1-(1+i)^{-n}}{i}\) | Value today of end-of-period payments. |
| Annuity due FV | \(FV=A\dfrac{(1+i)^n-1}{i}(1+i)\) | Payments at the start of each period. |
| Annuity due PV | \(PV=A\dfrac{1-(1+i)^{-n}}{i}(1+i)\) | Present value of start-of-period payments. |
| Payment from FV | \(A=\dfrac{FV\cdot i}{(1+i)^n-1}\) | Required deposit to reach a target future value. |
| Payment from PV | \(A=\dfrac{PV\cdot i}{1-(1+i)^{-n}}\) | Payment for a present-value loan or payout. |
| APR to EAR | \(EAR=(1+r/m)^m-1\) | Convert nominal APR to effective yearly return. |
| EAR to APR | \(r=m((1+EAR)^{1/m}-1)\) | Find equivalent nominal APR for a frequency. |
| Continuous compounding | \(FV=PV e^{rt}\) | Compare the continuous limit with discrete compounding. |
Worked Examples
Savings with monthly compounding: 10,000 at 6% APR compounded monthly for 10 years gives \(FV=10000(1+0.06/12)^{120}\approx 18193.97\). Interpretation: about 8,193.97 is interest before taxes or fees.
Loan discounting to present value: A 25,000 payment due in 5 years at 7% annual discount rate has \(PV=25000/(1.07)^5\approx 17824.66\). A buyer paying more than that is accepting a lower return.
Ordinary annuity deposits: Depositing 100 at the end of each month for 10 years at 6% APR compounded monthly gives \(FV=100((1.005)^{120}-1)/0.005\approx 16387.93\).
Annuity due rent payments: A 1,200 rent payment at the start of each month for 12 months discounted at 0.5% per month has \(PV=1200(1-(1.005)^{-12})/0.005(1.005)\approx 14005.87\).
APR to EAR: 12% APR compounded monthly gives \(EAR=(1+0.12/12)^{12}-1\approx 12.6825\%\), so the effective yearly rate is higher than 12%.
Required rate: To grow 5,000 to 7,500 in 6 years, \(i=(7500/5000)^{1/6}-1\approx 6.9915\%\) per year.
Common Mistakes
- Mixing annual and monthly units: 6% per year is not 6% per month. Use APR and frequency or convert to periodic rate first.
- Confusing PV and FV: PV is the value today; FV is the value at the end of the term.
- Ignoring payment timing: Annuity due payments are one period earlier than ordinary payments and produce a higher value when rates are positive.
- Expecting taxes or inflation: Results are nominal unless you adjust the rate or cash flows yourself.
- Reading APR as EAR: APR is nominal; EAR includes the compounding effect.
When to Use PV vs FV
Use future value when you want to know what an investment or savings plan may become. Use present value when you want to compare a future payment, bond cash flow, loan payoff, lease, or investment target to money today.
FAQ
What is discrete compounding?
Discrete compounding adds interest at set intervals such as annually, monthly, weekly, or daily. This calculator converts annual rates into the matching periodic rate before applying standard time value of money formulas.
How is discrete compounding different from continuous compounding?
Discrete compounding applies interest a finite number of times per year. Continuous compounding is the mathematical limit where interest is applied constantly and uses \(e^{rt}\).
How do I convert APR to a periodic rate?
For nominal APR with \(m\) compounding periods per year, divide APR by \(m\). For example, 6% APR compounded monthly gives 0.5% per month.
What does compounding frequency mean?
Compounding frequency is how often interest is credited. More frequent compounding usually increases the effective annual rate for the same nominal APR.
What is an ordinary annuity vs annuity due?
Ordinary annuities pay at the end of each period. Annuity due payments occur at the start, so they earn one extra period of interest and are multiplied by \(1+i\).
Why do PV and FV signs differ in financial calculators?
Financial calculators often treat money paid out as negative and money received as positive. This page asks for positive amounts and explains the direction in the result interpretation.
How do I calculate time to double?
For periodic rate \(i\), time to double is \(n=\ln(2)/\ln(1+i)\). With an annual effective rate, use \(n=\ln(2)/\ln(1+EAR)\).
Do results include taxes, fees, inflation, or variable rates?
No. Results are educational estimates using the values entered. Add fees manually and adjust rates separately for inflation, taxes, or variable-rate assumptions.