This financial calculator resolves any time value of money problem like estimating the future value (FV), present value (PV) annuity payment (PMT) return rate or no. of periods. There is in depth info on this topic below the application form.

## How does this financial calculator work?

By applying the time value of money this tool helps in finding the right solution for any situation like the ones provided here:

- Approximating the amount you need to invest at the start of an investment plan in order to achieve by recurrent annuity payments a certain future value. For instance this tool may help you figure out which is the initial deposit you should be making to reach a certain amount in your saving account over a specific period of time and assuming a fixed interest and a regular monthly contribution.
- Calculating the present value (PV) of a future value (FV) in order to see how much a future amount worth in today’s money;
- Estimating how much an investment will generate at the end by assuming a starting deposit plus regular investments during a specific time frame and by a fixed rate of return;
- Calculating the interest rate or the return rate of an investment by assuming your efforts (initial investments plus regular contributions) and the revenue generated during a specific number of periods;
- No. of periods of an investment by knowing the starting cost, regular contributions value, its total revenue generated and the expected return percentage;
- Forecasting the Annuity Payment (PMT) required to achieve a certain amount in your account at the end of the period you specify;

The algorithm behind this financial calculator requires that ONLY 4 from the above 5 fields to be provided, while the variable to be calculated should be left blank:

- Starting principal/investment (PV) – this is the present value or the initial cost of the investment or the initial deposit in case of savings accounts.
- Annuity payment (PMT) refers to the regular payments that the investment will require. Depending on their frequency they can be monthly, annually, quarterly, semi-annually or any other interval but please remember that this frequency dictates the final number of periods. In other words the two figures (annuity payment and number of periods) should be correlated.
- Future value represents how much revenue the investment/deposit/business/savings account will generate at the end of the period in question.
- Interest rate or the return rate figure.
- Term - number of periods which is the term in years the investment or deposit is planned.
- Number of annuity payments per year (any from 1 to 12 payments/year).
- Compound interval that can be from Daily to Annually and refers to how quickly the interest/return gets capitalized and starts generating income.
- Payment/investing moment represents the moment when the annuity payment is made and can be either at the beginning or at the end of each period.

## Example of scenario calculations

Scenario 1 for calculating the future value of a deposit with monthly contributions:

An individual starts with an initial deposit of $10,000 (PV) while his fixed monthly contribution (q=12) to the savings account will be $,1000 (PMT) over the next 10 years (t) (no. of periods is 120 = 10 years * 12). Considering that the expected rate of return in average will be of 4% (r) (compounded monthly) (cf) and that all his monthly adds will take place at the beginning of each month let’s discover how much will he end up with in account right before retiring:

■ Future Value (FV) = $162,648.96

■ Present Value (PV) of the future value: $109,099.41

■ No. of annuity payments / periods (NP): 120

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

■ Annuity payment (PMT): $1,000.00

■ Starting principal invested: $10,000.00

■ Total principal invested: $20,000.00

■ Total interest earned/return on investment: $142,648.96

Scenario 2 for calculating how much an investor should deposit initially to reach a certain future value:

Let’s assume that an investor would like to end up with a balance of $100,000 (FV) in 5 years (t) from now, by contributing at the end of each month with $1,500 (PMT). Which is the value of the initial deposit he should be making if the interest rate is expected to be 3% (r) (compounded monthly) (cf)?

■ At the beginning you will need to invest $2,608.37 in order to reach your future value of $100,000.00

■ Future Value (FV): $100,000.00

■ Present Value (PV) of the Future Value: $86,086.91

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

■ Annual interest/return rate (r) (compound Annually): 3.0416%

■ Annuity payment (PMT): $1,500.00

■ Starting principal invested: $2,608.37

■ Total principal invested: $10,108.37

■ Total interest earned/return on investment: $89,891.63

Scenario 3 for calculating the effective rate of return a business generates:

What if analyzing an investment that is expected to generate a total revenue of $200,000 (FV) within 10 (t) years, while its starting cost is $50,000 (PV) and requires monthly investments of $500 (PMT) made at the beginning of each period with the interest compounded annually (cf):

■ In order to reach a future value of $200,000.00 the investment’s annual interest/return rate (compound Annually) should be 14.2937%

■ Future Value (FV) = $200,000.00

■ Present Value (PV) of the future value: $52,578.44

■ No. of payments / periods (NP): 10

■ Annual interest/return rate (IR) (compound Annually): 14.2937%

■ Annuity payment (PMT): $500.00

■ Starting principal invested: $50,000.00

■ Total principal invested: $55,000.00

■ Total interest earned/return on investment: $145,000.00

13 Mar, 2015