Web-based Financial Calculator: Time Value of Money

This Financial calculator employs the general financial formula: (PV + PMT(1 + c·IR)/IR)((1 + IR)^NP - 1) + PV + FV = 0, to calculate one of the 5 parameters when 4 parameters are known.

PV (Present Value): The current value of a future sum of money or stream of cash flows given a specified rate of return.
FV (Future Value): The value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today.
PMT (Periodic Payment): The amount paid per period in a financial transaction.
NP (Number of Periods): The total number of payment periods in an investment or loan.
IR (Interest Rate): The yearly rate charged by a lender to a borrower or paid by an investor.
c (beginning of period payments): is one if Begining of period of payments is selected otherwise 0.

Notice: the IR in the financial formula is the effective interest rate per period. A negative value for owed balance and money paid to the account, a positive value for balances in your favor, or withdrawal from the account.

Financial Calculator vs. 3.1

Money Manager Manager:

Parameters Present Value (PV)
Future Value (FV)
Periodic Payment (PMT)
Number of Periods (NP)
Interest Rate (IR)

Options Beginning of period payments
End of period payments

Continuous compounding
Discrete compounding

Compounding & Payment Options Compounding:
Payments:
Keep frequency the same

Display Options Display Annuity: Verbose:

Result
Plot Overview
Plot Payment Schedule
Help

Time Value of Money.

See the corresponding paper under the Papers link in the left sidebar or click on this link: Download paper

Notice: Negative value for owed balance and money paid to the account, positive value for balances in your favor, and withdrawal from the account. This is very important to notice. In the default example where PV=100,000 this indicates a loan from the bank of $100,000, since the bank is given you the money the value is positive, consequently, any period payment is negative since you are paying off the loan by paying back the bank the PMT value, which in this case is -$5783.01. The FV is in this example $0 since you continue PMT until the loan is paid off. However, if we assume that you only pay e.g. -$5000 per PMT then pressing Calc FV gives a balloon payment of -$43,915.06 as the final payment. As you can see the value is negative indicating that you owed the bank that amount. Remember, always know how to interpret positive and negative values.

Basic financial formulas: CF=Compound frequency, PF=payment frequency, c=1 for beginning of period payment otherwise 0, i=effective interest
Financial equation: (General)
(1): (PV+PMT(1+c·i)/i)((1+i)^NP-1)+PV+FV=0
by using:
(2): A=(1+i)^NP-1
(3): B=(1+c·i)/i
you get:
(4): (PV+PMT*B)*A+PV+FV=0
which solved for the other variable gives:
(5): NP=log((PMT*B-FV)/(PMT*B+PV))/log(1+i)
(6): PV=-(FV+A*PMT*B)/(A+1)
(7): PMT=-(FV+PV(A+1))/(A*B)
(8): FV=-(PV+A(PV+PMT*B)).
(9): IR solved by iteration

Please email me if you encounter any problems at hve@hvks.com

Corrections:

4-Oct-2024	vs 3.1	Change the IR calculation trhough iteration to a more stable iteration
15-May-2024	vs 3.0	Completely rewritten and expanded internally with the use of the new Financial object library, plus added the Plot overview and Plot of payment schedule. The textual table with breakdown of each period has been beautified
23-Feb-2022	vs 2.12	Fix an issue calculating IR when compounding was monthly. The result was 12 times less
16-Feb-2022	vs 2.11	Fix an issue calculating IR when PMT was 0 and also fix some incorrect display text
15-Aug-2020	vs 2.10	Fix an issue with printing on some browsers
24-Apr-2020	vs 2.9	Added total payment and total interest for annuities display
7-Nov-2019	vs 2.8	Redesign GUI
20-May-2018	vs 2.6	Fixed an issue with the interest iteration
23-Apr-2018	vs 2.5	Added new history retrieve for PV, FV, PMT, NP, and IR
27-Sep-2016	vs 2.4	Bugs fixed.
18-Sep-2016	vs 2.3	Rewrote the iteration for interest. Now it is faster and more robust.
14-Sep-2014	vs 2.2	Fixed a reported bug in the calculation of the interest rate.
12-Oct-2011	vs 2.0	Fixed several bugs thanks to Franz Huber's input, including a bug with interest calculation and other used formulas.
9-Oct-2011	vs 1.8	Fixed a bug with the beginning and end of the period calculation.
9-Oct-2011	vs 1.7	Fixed a bug in the FV formula.