This finance calculator can perform any time value of money calculation: finding the present value (PV), future value (FV), annuity payment (PMT) interest rate or no. of periods. There is more information on this topic below the tool.

## How does this finance calculator work?

This is a handy time value of money calculator that allows you to make any of the following financial calculations:

- Estimating the starting principal to be invested in a business or opportunity;
- Calculating the present value (PV) of a given future value;
- Finding the future value (FV) of a given present value and/or series of annuity payments;
- Forecasting the annuity payment (PMT);
- Estimating the interest rate/rate of return of a business;
- Finding the number of periods required and the total interest/return an investment may generate.

Depending on the figure you would like to determine, you have to input values ONLY in 4 fields from the existing ones, to get the right value for the 5^{th} variable in the financial problem you are trying to resolve.

This finance calculator is very flexible as it allows choosing between different compounding interest frequencies such as: Daily, Weekly, Monthly, Quarterly, Semiannually or Annually; and also a desired moment when the annuity payments take place: at the beginning of each period or at the end of them. This is related to the two annuity payment types:

- Ordinary annuity – the payment is made at the end of each period over a fixed time frame.
- Annuity due – the payment is made at the end of beginning of each period over a fixed period of time.

## Time value of money terminology (TVM)

In finance the time value of money is a calculation made with the scope to solve for one of several variables in a financial problem. Apart from the standard financial terminology, the one specifically related to TVM may include:

- Compound Interest - is the interest type in which the earnings from the previous period are capitalized, and so the rate the money can grow is exponential.
- Compounding frequency – refers to how often the interest is capitalized to the principal. Can be any from Daily to Annually.
- Discount rate – is the interest rate (return rate) used to figure out the future or present values by case.
- Future value (FV) – indicates the value of a cash flow (or of a series of payments /cash flows) within a given time frame. In order words this figure indicates how much a business or investment will generate in the future until a certain point in time.
- Net present value (NPV) – is a value that shows the present value of the future cash flows generated by a business minus the cost associated with the investment. It demonstrates how much economic profit an investment will generate, thus the NPV should be at least equal than zero, if not greater for the investment to be considered viable in the eye of an investor
- Number of periods – is the count of the periods of the financial problem to be solved and is SHOULD NOT confused with the number of years. For instance in case of a personal loan taken over 3 years, with monthly payments, thus the number of periods is considered to be 3*12 = 36 periods. As it can easily be observed a period is considered to be a unit of time with a specific length that varies from one product/problem to another. The length in time of the period is equal to the time that passes between the cash flows.
- Payment – is considered the amount of money resulting of the cash flow.
- Present value (PV) – represents the value in today’s money of a future value/ a series of future cash flows. IN order words this is the value you should pay today in order to get a certain amount in the future.

## Example of calculations

Scenario 1 for calculating the future value:

Assuming someone decides to invest $100,000 (PV) over a period of 5 years (t) while contributing annually (q=1) with $10,000 (PMT) in his savings account at the beginning of each year. The annual interest rate offered by the bank is 3.5% (r) while its compounding interval is quarterly (cf). Let’s figure out his ending balance after 5 years:

■ Future Value (FV) = $174,611.59

■ Present Value (PV) of the future value: $146,690.54

■ No. of annuity payments / periods (NP): 5

■ Annual interest / return rate (r) (compound Annually): 3.5462%

■ Annuity payment (PMT): $10,000.00

■ Starting principal invested: $100,000.00

■ Total principal invested: $150,000.00

■ Total interest earned/return on investment: $24,611.59

Scenario 2 for calculating the present value of a future value:

Let’s figure out how much does an individual need to invest in today’s money (one time deposit) in order to achieve in the future a savings goal in the account of $100,000 (FV) in case his monthly contribution (q=12) is set up at $1,000 (PMT) per month (at the end of each month), the average interest rate is expected to be of 4.5% (r) compounded monthly (cf) and the time period to achieve the goal is 5 years (t):

■ At the beginning you will need to invest $26,245.85 in order to reach your future value of $100,000.00

■ Future Value (FV): $100,000.00

■ Present Value (PV) of the Future Value: $79,885.23

■ No. of annuity payments / periods (NP): 60

■ Annual interest/return rate (r) (compound Annually): 4.5940%

■ Annuity payment (PMT): $1,000.00

■ Starting principal invested: $26,245.85

■ Total principal invested: $31,245.85

■ Total interest earned/return on investment: $68,754.15

Scenario 3 for calculating the required rate of return in specific conditions:

Let’s figure out which is the return rate of an investment in case the starting principal to be invested is $100,000 (PV), the annual contribution to the investment is $10,000 (PMT) at the end of each year (q=1), over the next 10 years (t), while the investment is expected to generate in total an amount of $300,000 (FV) if it is compounded semi-annually (cf):

■ In order to reach a future value of $300,000.00 the investment’s annual interest/return rate (compound Semiannually) should be 5.4453%

■ Future Value (FV) = $300,000.00

■ Present Value (PV) of the future value: $175,306.06

■ No. of payments / periods (NP): 10

■ Annual interest/return rate (IR) (compound Annually): 5.5194%

■ Annuity payment (PMT): $10,000.00

■ Starting principal invested: $100,000.00

■ Total principal invested: $200,000.00

■ Total interest earned/return on investment: $100,000.00

Scenario 4 for calculating the annuity payment required for achieving specific FV:

Let’s discover how much an individual should contribute to his savings account on a monthly basis (q=12) (at the beggining of each month) in order to achieve at the end of 120 months/10 years (t) a balance of $100,000 (FV) knowing that his starting principal deposited is $15,000 (PV) and that the average interest rate is 4% (r) compounded monthly (cf):

■ In order to reach a future value of $100,000.00 you will need to contribute with 12 payments/year at the End of each period, in amount of $527.25 each payment

■ Future Value (FV) = $100,000.00

■ Present Value (PV) of the future value: $67,076.61

■ No. of payments / periods (NP): 120

■ Annual interest/return rate (r) (compound Annually): 4.0742%

■ Annuity payment (PMT): $527.25

■ Starting principal invested: $15,000.00

■ Total principal invested: $20,272.50

■ Total interest earned/return on investment: $79,727.50

Scenario 5 for calculating the required time period in certain conditions:

An individual can save monthly an amount of $500 (PMT) (saved at the beggining of each month) - (q=12), he can also make an initial investment of $1,000 (PV). Let's calculate how many periods (months) are required to achieve an amount of $50,000 (FV) in case the rate of return on investment is considered to be 5% (r), compounded monthly (cf):

■ In order to reach a future value of $50,000.00 the number of years you have to invest/contribute is 7 (which is equivalent to 81 payments/periods) while the interest is compounded Monthly.

■ Future Value (FV) = $50,000.00

■ Present Value (PV) of the future value: $35,630.50

■ No. of payments / periods (NP): 81

■ Annual interest/return rate (IR) (compound Annually): 5.1162%

■ Annuity payment (PMT): $500.00

■ Starting principal invested: $1,000.00

■ Total principal invested: $41,743.17

■ Total interest earned/return on investment: $8,256.83

09 Mar, 2015