what is the time value of money tvm 
the time value of money tvm is the concept that a sum of money is worth more now than the same sum will be at a future date due to its earning potential in the interim because money can grow when it is invested a delayed payment is a lost opportunity for growth the time value of money is a core principle of finance it is also referred to as the present discounted value understanding the time value of money tvm most investors would rather receive money today than wait to receive the same amount in the future that s because a sum of money once invested can grow over time for example money deposited into a high yield savings account will earn interest over the ensuing months and years that interest will be added to the principal earning even more interest that s what s known as the power of compound interest in addition if money is not invested its value can erode over time if you hide 1 000 in a mattress for three years you will not only lose out on any additional money you could have earned by investing it but it will have even less buying power than it once did because inflation will have reduced its value the concept of the time value of money is often attributed to martin de azpilcueta a spanish theologian and economist of the 16th century 12time value of money formulathe basic time value of money formula doesn t calculate tvm itself instead it shows the change in the value of money over a period of time it calculates the future value of a sum of money based on based on these variables the tvm formula is f v p v 1 i n n t where f v future value of money p v present value of money i interest rate n number of compounding periods per year t number of years begin aligned fv pv big 1 frac i n big n times t textbf where fv text future value of money pv text present value of money i text interest rate n text number of compounding periods per year t text number of years end aligned fv pv 1 ni n twhere fv future value of moneypv present value of moneyi interest raten number of compounding periods per yeart number of years this allows you to see the difference between the future value and the present value in most cases the future value will be higher which is why it is better to receive that money now rather than at a later date the tvm formula may change slightly depending on the situation for example in the case of annuity or perpetuity payments the generalized formula will have additional or fewer factors the time value of money doesn t take into account any capital losses that you may incur or any negative interest rates that may apply in these cases you may be able to use negative growth rates to calculate the time value of moneyexamples of time value of moneyassume a sum of 10 000 is invested for one year at 10 interest compounded annually the future value of that money is f v 10 000 1 10 1 1 1 11 000 begin aligned fv 10 000 times big 1 frac 10 1 big 1 times 1 11 000 end aligned fv 10 000 1 110 1 1 11 000 the formula can also be rearranged to find the value of the future sum in present day dollars for example the present day dollar amount compounded annually at 7 interest that would be worth 5 000 one year from today is p v 5 000 1 7 1 1 1 4 673 begin aligned pv big frac 5 000 big 1 frac 7 1 big big 1 times 1 4 673 end aligned pv 1 17 5 000 1 1 4 673 the number of compounding periods has a dramatic effect on the tvm calculations taking the 10 000 example above if the number of compounding periods is increased to quarterly monthly or daily the ending future value calculations are this shows that the tvm depends not only on the interest rate and time horizon but also on how many times the compounding calculations are computed each year 