Time Value of Money

Number of Months/Years

Interest per Month/Year

Present Value

Payments

Future Value

*(Enter any 4 values to calculate the other),
*(PV is set as negative by default indicating cash outflow, please enter negative value to indicate cash inflow)

What is the Time Value of Money?

The time value of money is a concept that demonstrates some value associated with money w.r.t time.

If you are offered some money, let's say 100 now and an option to have the same amount 1 year from today, you'll choose to have it today as you can earn interest on offered money and make some extra money out of it through interest.

The time value of money is a concept that lies at the heart of finance. It has broad applications in the valuation of all securities. It enables us to answer questions like how much is the amount today worth after X years, what is the worth of Y amount today that is yet to be received X years from now, and numerous more. The SIP calculator and EMI calculator implemented here are examples of using time value of money calculations.

How to use TVM Calculator?

The above arrangement of text boxes is same as the placement of keys on a Texas BA 2 plus calculator. You can similarly enter values as you do on BA 2 plus except for the fact that the present value is taken as a negative value by default for easy calculations.

For those who are not aware of how BA 2 plus works, let's get into what the fields are and their significance -

Number of Months/Years (N) - You can enter the value as a number of months if the interest rate is monthly or you can enter the value as a number of years if the interest rate is yearly.

Interest rate (I/Y) - It is the interest rate or required rate per year or per month.

Present Value (PV) - Present Value is as the name suggest, the present value of any future money or value of any cash at present

Payment (PMT) - Payment is the equal cash that is being paid or received at every month or year

Future Value (FV) - Future value is the value of present money and any payment made in between in future considering compounding

Example to calculate future value

This example shows how we can use above tool to calculate future value

Situation - Let's consider we have initial capital of 1,00,000 and want to invest it in a security that gives 8% return per year for 10 years and we want to find the value of our money at the end of year 10.

Solution - To calculate the final value at the end of year 10, we need to put value of N as 10 as number of years are 10, value of I/Y as 8% as we get return of 8% every year, present value as -1,00,000 (- sign indicating cash outflow which is default convention implemented so we enter just 1,00,000 in the text box) , payment as 0 as we haven't received nor paid any amount. Since we need to calculate future value keep the field blank and hit the calculate button to get value at the end of year 10.

Example to calculate interest

This example shows how we can use above tool to calculate interest

Situation - Let's consider we have initial capital of 1,00,000 and after 10 years after investing in some place the final value (future value) after the end of year 10 will be 2,00,000 and we are investing a fixed amount of 1000 per year and we want to find out what is the rate per year (I/Y)

Solution - To calculate the interest rate (I/Y) as we have given an initial value of 1,00,000 we can put PV as 1,00,000 in the above text box of PV(-ve sign indicates cash outflow), put N as 10 as the number of years is 10, payment (PMT) as -1000 (-ve as cash going outs) and future value as 2,00,000 in future value. Hit calculate button to get the interest earned per year which is - 7.17%

Example to calculate present value

This example shows how we can use above tool to calculate present value

Situation - Let's consider we have need a capital of 1,00,000 and we are investing 10,000 at the end of every year (pmt=10,000) at the rate of 10% we need to find the amount that we can invest today to achive the desired outcome, what that value could be?

Solution - To calculate the present value we have a future value (FV) of 1,00,000 and we are investing 10,000 after every year implying a payment of 1,000 i.e PMT is -1,000(-ve as cash outflow) for 10 years (N = 10) with interest rate of 10% (I/Y = 10%) to calculate the amount that we need to invest today (PV) enter the corresponding values and hit calculate button to obtain the present value which would be -32,409.76.

Example to calculate payments

This example shows how we can use above tool to calculate payments for each period

Situation - Let's assume we require a capital of 2,50,000. Currently, we are investing 1,00,000 to reach 2,50,000 at the end of 5 years (N = 5) for a specific purpose. We have identified an investment that will yield a 10% return annually (I/Y = 10%). What is the additional amount needed to be invested each year to attain the final value (future value) of 2,50,000?

Solution - To calculate the necessary payment to reach 2,50,000, set 1,00,000 as the present value (PV), 5 as the number of years (N) for the investment period, 10 as the interest rate per year (I/Y) representing the 10% return, and 2,50,000 as the future value (FV). After hitting the calculate button, the result is 14,569.62. This is the amount that must be invested at the end of every year to achieve the future value of 2,50,000.

Example to number of years

This example shows how we can use above tool to calculate number of years

Situation - Let's assume we require a capital of 10,00,000. Currently, we are investing 5,00,000 as initial investment with 10% return annually. If we are considering to invest 1,00,000 every year, how many years are required to get to the amount of 10,00,000 as future value?

Solution - To calculate the years to reach 10,00,000, set 10,00,000 as FV, 10 as I/Y as return is 10%, 1,00,000 as PV as initial investment is 1,00,000 and 1,00,000 as PMT as we are paying 1,00,000 at the end of each year. Hit calculate to get the number of years required to get to the final value of 10,00,000, you would get N as 2,50,000.