This finance calculator can be used to calculate any one of the parameters of future value (FV), number of compounding periods (N), interest rate (I/Y), annuity payment (PMT), and starting investment if other parameters are known. The present value will always be given out. Each of the following tabs represents the parameters to be calculated.
FV (Future Value)
PV (Present Value)
N (Number of Periods)
I/Y (Interest Rate)
PMT (Periodic Payment)
Balance Accumulation Graph
The Time Value of Money
Suppose someone owes you $500. Would you rather have this money repaid to you right away, in one payment, or spread out over a year in four installment payments? How would you feel if you had to wait to get the full payment, instead of getting all at once? Wouldn’t you feel that the delay in the payment cost you something?
According to a concept that economists call the “time value of money,” you would probably be right. You want your money right away, in one payment. You could do what you wanted to with the money: Spend it on something you wanted to buy, or invest this money and earn interest on it or you could use this money to pay off all or part of a loan. There are a million things you could do with this money, and it would be your choice. The “time value of money” refers to the fact that a dollar in hand today is worth more than a dollar promised at some future time.
This is the basis of the concept of interest payments, the fact that when you deposit your money in a bank, you receive a payment for leaving the money on deposit there. The bank is paying you a small dividend for having that money at hand.
This is also why the bank will pay you more for keeping the money in longer, and for committing to keeping the money in for a fixed period.
The value that your money will have at the end of a period of collecting interest is called its Future Value in finance. Here is how it works.
Suppose you invest $100 in a savings account that pays 10% interest per year. How much will you have in one year? You will have $110. This $110 is equal to your original principal of $100 plus $10 in interest. We say that $110 is the future value of $100 invested for one year at 10%, meaning that $100 today is worth $110 in one year, given that the interest rate is 10%.
In general, if you invest for one period at an interest rate r, your investment will grow to (1 + r) per dollar invested. In our example, r is 10%, so your investment grows to 1 + 0.10 = 1.10 dollars per dollar invested. You invested $100 in this case, so you ended up with $100 x 1.10 = $110.
Consider your $100 investment that has now grown to $110. If you keep that money in the bank, what will you have after two years, assuming the interest rate remains the same? You will earn $110 x 0.10 = $11 in interest after the second year, making a total of $110 + $11 = $121. This $121 is the future value of $100 in two years at 10%. Another way of looking at it is that one year from now, you are effectively investing $110 at 10% for a year. This is a single-period problem, so you will end up with $1.10 for every dollar invested, or $110 x 1.1 = $121 total.
Similarly, the Present Value (PV) in finance is what the future money will worth now at given interest rate. In this case the present value of $121 two years later with 10% interest rate is $100.
This $121, or the Future Value (FV) of your money, has four parts.
- The first part is the first $100 original principal, or its Present Value (PV);
- The second part is the $10 in interest you earned in the first year.
- The third part, is the other $10 you earn in the second year, for a total of $120.
- The fourth part is $1 which is interest you earned in the second year on the interest paid in the first year: ($10 x 0.10 = $1)
In the real world, it is normally more complex than the cases above. You may have a rental property bring in a rental income of $1,000 per month. This recurring cash flow is called annuity payment (PMT). People may wonder what the cash flow of $1,000 per month for 10 years worth? Or how to evaluate the value of a business that generates $100 income every year? Or if you pay a down payment of $30,000 and a monthly mortgage of $1,000, what the property should worth after 30 years? This finance calculator can help in evaluating all these situations. Some even more situations can normally be broken down into a few simple cases and add the results together.