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Make sure you get the basics; be able to apply the formulae for determining present and future value.

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The time value of money (TVM) is the concept that money available at the present time is worth more than the identical sum in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received. TVM is also sometimes referred to as present discounted value.

The time value of money draws from the idea that rational investors prefer to receive money today rather than the same amount of money in the future because of money's potential to grow in value over a given period of time. For example, money deposited into a savings account earns a certain interest rate, and is therefore said to be compounding in value.

Further illustrating the rational investor's preference, assume you have the option to choose between receiving $10,000 now versus $10,000 in two years. It's reasonable to assume most people would choose the first option. Despite the equal value at time of disbursement, receiving the $10,000 today has more value and utility to the beneficiary than receiving it in the future due to the opportunity costs associated with the wait. Such opportunity costs could include the potential gain on interest were that money received today and held in a savings account for two years.

Depending on the exact situation in question, the TVM formula may change slightly. For example, in the case of annuity or perpetuity payments, the generalized formula has additional or less factors. But in general, the most fundamental TVM formula takes into account the following variables:

FV = Future value of money

PV = Present value of money

i = interest rate

n = number of compounding periods per year

t = number of years

Based on these variables, the formula for TVM is:
FV = PV x [ 1 + (i / n) ] (n x t)
Assume a sum of $10,000 is invested for one year at 10% interest. The future value of that money is:

FV = $10,000 x (1 + (10% / 1) ^ (1 x 1) = $11,000

The formula can also be rearranged to find the value of the future sum in present day dollars. For example, the value of $5,000 one year from today, compounded at 7% interest, is:

PV = $5,000 / (1 + (7% / 1) ^ (1 x 1) = $4,673

The number of compounding periods can have a drastic 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:

Quarterly Compounding: FV = $10,000 x (1 + (10% / 4) ^ (4 x 1) = $11,038

Monthly Compounding: FV = $10,000 x (1 + (10% / 12) ^ (12 x 1) = $11,047

Daily Compounding: FV = $10,000 x (1 + (10% / 365) ^ (365 x 1) = $11,052

This shows TVM depends not only on interest rate and time horizon, but also on how many times the compounding calculations are computed each year.

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The time value of money (TVM) is the concept that money available at the present time is worth more than the identical sum in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received.

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Congratulations!!! You have won a cash prize! You have two payment options: A - Receive $10,000 now OR B - Receive $10,000 in three years. Which option would you choose?

If you're like most people, you would choose to receive the $10,000 now. After all, three years is a long time to wait. Why would any rational person defer payment into the future when he or she could have the same amount of money now? For most of us, taking the money in the present is just plain instinctive. So at the most basic level, the time value of money demonstrates that, all things being equal, it is better to have money now rather than later.

But why is this? A $100 bill has the same value as a $100 bill one year from now, doesn't it? Actually, although the bill is the same, you can do much more with the money if you have it now because over time you can earn more interest on your money.

Back to our example: by receiving $10,000 today, you are poised to increase the future value of your money by investing and gaining interest over a period of time. For Option B, you don't have time on your side, and the payment received in three years would be your future value. To illustrate, we have provided a timeline:

If you are choosing Option A, your future value will be $10,000 plus any interest acquired over the three years. The future value for Option B, on the other hand, would only be $10,000. So how can you calculate exactly how much more Option A is worth, compared to Option B? Let's take a look.

If you choose Option A and invest the total amount at a simple annual rate of 4.5%, the future value of your investment at the end of the first year is $10,450, which of course is calculated by multiplying the principal amount of $10,000 by the interest rate of 4.5% and then adding the interest gained to the principal amount:

Future value of investment at end of first year:

= ($10,000 x 0.045) + $10,000

You can also calculate the total amount of a one-year investment with a simple manipulation of the above equation:

Original equation: ($10,000 x 0.045) + $10,000 = $10,450

Manipulation: $10,000 x [(1 x 0.045) + 1] = $10,450

Final equation: $10,000 x (0.045 + 1) = $10,450

The manipulated equation above is simply a removal of the like-variable $10,000 (the principal amount) by dividing the entire original equation by $10,000.

If the $10,450 left in your investment account at the end of the first year is left untouched and you invested it at 4.5% for another year, how much would you have? To calculate this, you would take the $10,450 and multiply it again by 1.045 (0.045 +1). At the end of two years, you would have $10,920:

Future value of investment at end of second year:

The above calculation, then, is equivalent to the following equation:

Future Value = $10,000 x (1+0.045) x (1+0.045)

Think back to math class and the rule of exponents, which states that the multiplication of like terms is equivalent to adding their exponents. In the above equation, the two like terms are (1+0.045), and the exponent on each is equal to 1. Therefore, the equation can be represented as the following:

We can see that the exponent is equal to the number of years for which the money is earning interest in an investment. So, the equation for calculating the three-year future value of the investment would look like this:

This calculation shows us that we don't need to calculate the future value after the first year, then the second year, then the third year, and so on. If you know how many years you would like to hold a present amount of money in an investment, the future value of that amount is calculated by the following equation:

If you received $10,000 today, the present value would, of course, be $10,000 because the present value is what your investment gives you now if you were to spend it today. If $10,000 were to be received in a year, the present value of the amount would not be $10,000 because you do not have it in your hand now, in the present. To find the present value of the $10,000 you will receive in the future, you need to pretend that the $10,000 is the total future value of an amount that you invested today. In other words, to find the present value of the future $10,000, we need to find out how much we would have to invest today in order to receive that $10,000 in the future.

To calculate the present value, or the amount that we would have to invest today, you must subtract the (hypothetical) accumulated interest from the $10,000. To achieve this, we can discount the future payment amount ($10,000) by the interest rate for the period. In essence, all you are doing is rearranging the future value equation above so that you may solve for P. The above future value equation can be rewritten by replacing the P variable with present value (PV) and manipulated as follows:

Let's walk backward from the $10,000 offered in Option B. Remember, the $10,000 to be received in three years is really the same as the future value of an investment. If today we were at the two-year mark, we would discount the payment back one year. At the two-year mark, the present value of the $10,000 to be received in one year is represented as the following:

Present value of a future payment of $10,000 at end of year two:

Note that if today we were at the one-year mark, the above $9,569.38 would be considered the future value of our investment one year from now.

Continuing on, at the end of the first year we would be expecting to receive the payment of $10,000 in two years. At an interest rate of 4.5%, the calculation for the present value of a $10,000 payment expected in two years would be the following:

Present value of $10,000 in one year:

Of course, because of the rule of exponents, we don't have to calculate the future value of the investment every year counting back from the $10,000 investment in the third year. We could put the equation more concisely and use the $10,000 as FV. So, here is how you can calculate today's present value of the $10,000 expected from a three-year investment earning 4.5%:

So the present value of a future payment of $10,000 is worth $8,762.97 today if interest rates are 4.5% per year. In other words, choosing Option B is like taking $8,762.97 now and then investing it for three years. The equations above illustrate that Option A is better not only because it offers you money right now but because it offers you $1,237.03 ($10,000 - $8,762.97) more in cash! Furthermore, if you invest the $10,000 that you receive from Option A, your choice gives you a future value that is $1,411.66 ($11,411.66 - $10,000) greater than the future value of Option B.

Let's add a little spice to our investment knowledge. What if the payment in three years is more than the amount you'd receive today? Say you could receive either $15,000 today or $18,000 in four years. Which would you choose? The decision is now more difficult. If you choose to receive $15,000 today and invest the entire amount, you may actually end up with an amount of cash in four years that is less than $18,000. You could find the future value of $15,000, but since we are always living in the present, let's find the present value of $18,000 if interest rates are currently 4%. Remember that the equation for present value is the following:

In the equation above, all we are doing is discounting the future value of an investment. Using the numbers above, the present value of an $18,000 payment in four years would be calculated as the following:

From the above calculation, we now know our choice is between receiving $15,000 or $15,386.48 today. Of course, we should choose to postpone payment for four years!

These calculations demonstrate that time literally is money - the value of the money you have now is not the same as it will be in the future and vice versa. So, it is important to know how to calculate the time value of money so that you can distinguish between the worth of investments that offer you returns at different times.

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Congratulations!!! You have won a cash prize! You have two payment options: A - Receive $10,000 now OR B - Receive $10,000 in three years. Which option would you choose? If you're like most people, you would choose to receive the $10,000 now. After all, three years is a long time to wait.

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The time value of money (TVM) is an important concept to investors because a dollar on hand today is worth more than a dollar promised in the future. The dollar on hand today can be used to invest and earn interest or capital gains. A dollar promised in the future is actually worth less than a dollar today because of inflation.

Provided money can earn interest, this core principle of finance holds that any amount of money is worth more the sooner it is received. At the most basic level, the time value of money demonstrates that, all things being equal, it is better to have money now rather than later.

Present value determines what a cash flow to be received in the future is worth in today's dollars. It discounts the future cash flow back to the present date, using the average rate of return and the number of periods. No matter what the present value is, if you invest that present value amount at the specified rate of return and number of periods, the investment would grow into the future cash flow amount.

Present value = (future cash flow) / (1+ rate of return)^number of periods

Future value determines what a cash flow received today is worth in the future, based on interest rates or capital gains. It calculates what a current cash flow would be worth in the future, if it was invested at a specified rate of return and number of periods.

Future value = present value x {1 + (rate of return x number of periods)}

Both present value and future value take into account compounding interest or capital gains, which is another important aspect for investors to consider when looking for good investments.

Time is literally money. The value of the money you have now is not the same as it will be in the future. Knowing how to determine TVM by calculating present and future value can help you distinguish between the worth of investments that offer returns at different times.

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Why the Time Value of Money (TVM) Matters to Investors

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The time value of money (TVM) is an important concept to investors because a dollar on hand today is worth more than a dollar promised in the future. The dollar on hand today can be used to invest and earn interest or capital gains.

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An inverted yield curve is an interest rate environment in which long-term debt instruments have a lower yield than short-term debt instruments of the same credit quality. This type of yield curve is the rarest of the three main curve types and is considered to be a predictor of economic recession.

A partial inversion occurs when only some of the short-term Treasuries (five or 10 years) have higher yields than 30-year Treasuries. An inverted yield curve is sometimes referred to as a negative yield curve.

Historically, inversions of the yield curve have preceded many of the U.S. recessions. Due to this historical correlation, the yield curve is often seen as an accurate forecast of the turning points of the business cycle. A recent example is when the U.S. Treasury yield curve inverted in late 2005, 2006, and again in 2007 before U.S. equity markets collapsed. The curve also inverted in late 2018. An inverse yield curve predicts lower interest rates in the future as longer-term bonds are demanded, sending the yields down.

Yields are normally higher on fixed-income securities with longer maturity dates. Higher yields on longer-term securities are a result of maturity risk premium because changes in the value of longer-term securities are more unpredictable with market interest rates potentially more unsettled over a longer time horizon. However, yields on longer-term securities could be trending down when market interest rates are set to get lower for a foreseeable future to accommodate ongoing weak economic activities. Irrespective of their reinvestment rate risk, shorter-term securities appear to offer higher returns than longer-term securities during such times.

The shape of the yield curve changes in accordance with the state of the economy. The normal or up-sloped yield curve may persist when the economy is growing and conversely, the inverted or down-sloped yield curve is likely to press on when the economy is in a recession. One underlying reason such a relationship exists between the yield curve and economic performance relates to how a higher or lower level of long-term capital investments may help stimulate or rein in the economy. By issuing longer-term securities with lower-yield offerings, businesses and governments alike can acquire needed investment capital at affordable costs to jump start a weak economy.

What moves yields in the market is the varying demands for securities of different maturities at a particular time and under given economic conditions. When the economy is heading to a recession, knowing interest rates are to trend lower, investors are more willing to invest in longer-term securities immediately to lock in current higher yields. This, in turn, increases the demand for longer-term securities, boosting their prices and further lowering their yields. Meanwhile, few investors want to invest in shorter-term securities when presented with lower reinvestment rates. With lower demand for shorter-term securities, their yields actually go up, giving rise to an inverted yield curve when yields on longer-term securities have come down at the same time.

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An inverted yield curve is an interest rate environment in which long-term debt instruments have a lower yield than short-term debt instruments of the same credit quality. This type of yield curve is the rarest of the three main curve types and is considered to be a predictor of economic recession.