This Time Value of Money calculator solves any TVM problem such as finding the present value (PV), future value (FV), annuity payment (PMT), interest rate or the no. of periods. There is more info on this topic below the form.

Instruction: Please input data ONLY in 4 fields from the 5 below in order to calculate the value for the value you want to calculate. Leave blank ONLY the field you want to estimate!

Present Value (PV):
Payment (PMT):
Future Value (FV):
Nominal Interest Rate (IR):
No. of periods (NP - e.g years):
Compounding frequency (CP):
Payment/investing moment:

## How does this Time Value of Money calculator work?

This finance calculator can solve for any unknown variable in a financial problem as explained below and to do so the user has to left blank ONLY one field.

Depending on the TVM calculation type, the algorithm behind this time value of money calculator applies these formulas:

• Estimating the present value (PV) by this equation:
• • Forecasting the future value (FV) by this formula:
• • Determining the Nominal Interest rate (IR) and No. of periods which are obtained from this equation:

• • Calculating the Payment (PMT) by this formula:
• Please take account of the fact that the no. of periods and nominal interest rate are extracted by using the Newton-Raphson method.

Where:

PV = present value / starting or initial amount invested or deposited.

FV= future value expected.

IR = interest rate per period. Please remember that the effective rate per period should refer to the time unit you consider in the No. of periods fields. For instance in case the no. of periods are considered to be months, then the interest rate per period should be monthly too.

NP = (No. of periods*CP)

k = is equal to 1 in case the Payment/Investment moment is ”End of period”; OR k = (1 + IR / (100 * CP) )  if the payment takes place at the “Beginning of period”.

CP is the coefficient for each compounding frequency:

- If Annually then CP = 1

- If Semiannually then CP = 2

- If Quarterly then CP = 4

- If Monthly then CP = 12

- If Weekly then CP = 54

## What is a TVM problem?

In finance, a TVM problem is a one that requires solving for an unknown variable out of several ones as presented here:

• Figure out the present value (initial investment) based on a given FV, PMT, IR, CP and NP;
• Determine a future value of a PV and a series of PMTs based on a PV, PMT, IR, CP and NP;
• Figure out how much to invest regulalry (PMT) considering a PV, FV, IR, CP and NP;
• Estimate the interest rate an investment/deposit or savings account will generate by considering the starting investment amount (PV), FV it generates, NP and CP;
• Calculate the number of periods an investment will require to reach a certain amount by taking account of a PV, FV, PMT, IR and CP.

## Example of time value of money calculations

### Scenario 1 FV: How much you will end up in a savings account with regular contributions?

Someone makes an initial deposit of \$10,000 (PV), then he makes regular contributions of \$1,000 (PMT) on a monthly basis at the beginning of each month over the next 5 years ( NP = 60 months). What will be the ending balance of his savings account in case the interest rate per month is considered 0.4%, compounded monthly?

Answer: Future Value (FV) = \$70,816.00

### Scenario 2 PV: How much to invest initially to reach a certain amount in account at the end?

An individual is willing to contribute at the beginning of each month with \$500 (PMT) over the next 10 years (NP = 120 months) in order to reach a savings goal of \$150,000 for his retirement. The question is how much should he deposit initially in case the interest rate per month is considered to be 0.35%, compounded monthly?

Answer: Present Value (PV) = \$85,870.66

### Scenario 3 PMT: How much to save regularly to achieve your savings goal in a given period of time?

An individual deposits initially an amount of \$5,000 and is willing to make contributions to his savings account at the end of each year over the next 15 years (NP = 15) in order to reach before retirement an amount of \$100,000. The question if how much will he need to deposit yearly in case the annual interest rate is considered to be 4.5%, compounded annually?

### Scenario 4 NP: How much time to invest to reach your goal?

Assuming someone makes and initial deposit of \$100,000 (PV) and that is available to contribute at the beginning of each year with \$5,000, the question is how many years will he need to keep saving in order to end up in account with \$250,000 in case the yearly interest rate is considered to be 3.95% compounded semi-annually?

Answer: No. of periods: 18 with Semiannually compounding frequency.

### Scenario 5 IR: What interest/return rate should an investment generate in order to reach certain future value?

Let’s consider that an individual deposits initially \$100,000 and that he makes at the end of each year an additional contribution of \$5,000 over the next 20 years. How much should the annual rate of return on his investment should be in order to end up in account with \$500,000?

Answer: Nominal interest rate (IR) = 5.94%.

07 Apr, 2015