time value of money, various concepts and summaries, a perfect cheat sheet for all you nee | Cheat Sheet Finance

The time value of money (TVM) is a useful tool in helping you understand the worth of money in

relation to time. It is a formula often used by investors to better understand the value of money as it

compares to its value in the future. Below we’ll go over the in’s and out’s of the TVM and how you

can use it to understand the effect time has on the value of your money.

Money today is worth more than money in the future. This is called the time value of money. There

are three reasons for the time value of money: inflation, risk and liquidity. As a result, borrowers

charge interest to ensure that the value of their money is not eroded by inflation, as a reward for

taking the risk of lending it out, and because the loan might not be easily sold to another borrower if

need be, that is, it has low liquidity. Another way of looking at interest is as the rental charged for

using someone else’s money.

What Is the Time Value of Money?

The basic principle of the time value of money is that money is worth more in the present than it is

in the future, because money you have now has the potential to earn. This is due largely in part to

inflation. If you think about it, $1,000 in 1999 could buy you more than it could 20 years later, in

2019. And having a $1,000 today will theoretically buy you more than having $1,000 five years from

now. With that in mind, the time value of money formula can help you determine the present value

of the money you have today and how much it could be worth in the future.

With investing, however, there is a certain amount of risk you should consider as you use the time

value of money. For example, saying you’ll take that $1,000 and invest it in your favorite company

that’s expected to provide a 5% return each year is not guaranteed. Instead, with this any

investment, you’re accepting the risk of losing money for the chance to beat inflation and increase

the future value of your money.

Why Is the Time Value of Money Important?

The time value of money is important because it allows investors to make a more informed decision

about what to do with their money. The TVM can help you understand which option may be best

based on interest, inflation, risk and return. It can also be used to help you understand how much

money to save in an account if you have a certain goal in mind, such as saving $20,000 in five years if

the account earns 3 percent compound interest each year.

The Importance of Compounding Interest

If the basic idea of the TVM is that money is worth more today than it is tomorrow, you’d think it’d

be wiser to spend it now rather than save it for later - but we know that isn’t always the case. While

inflation works against you, meaning it makes your dollar worth less tomorrow than today,

compound interest can work in your favor to elevate the value of your present dollar tomorrow.

With compounding interest, the amount of money you’re earning interest on grows in each

compounding period. For example, if you have $1,000 and it earns 10% compounding interest every

year for five years, the compounding period would be one year. While that means in the first you’ve

earned $100 in interest (10% of $1,000), in that second year you’re actually earning interest on the

total amount from the previous compounding period, which would be $1,100 (the original $1,000

plus the $110 in interest earned in year one). By the end of year two, you’d have earned $1,210

($1,100 plus $110 in interest). If you keep going until the end of year five, you would have turned

that $1,000 into approximately $1,610. If we consider that the highest inflation rate over the last 10

years was three percent, then in this scenario, choosing to invest your present money using

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The time value of money (TVM) is a useful tool in helping you understand the worth of money in relation to time. It is a formula often used by investors to better understand the value of money as it compares to its value in the future. Below we’ll go over the in’s and out’s of the TVM and how you can use it to understand the effect time has on the value of your money. Money today is worth more than money in the future. This is called the time value of money. There are three reasons for the time value of money: inflation , risk and liquidity. As a result, borrowers charge interest to ensure that the value of their money is not eroded by inflation, as a reward for taking the risk of lending it out, and because the loan might not be easily sold to another borrower if need be, that is, it has low liquidity. Another way of looking at interest is as the rental charged for using someone else’s money. What Is the Time Value of Money? The basic principle of the time value of money is that money is worth more in the present than it is in the future, because money you have now has the potential to earn. This is due largely in part to inflation. If you think about it, $1,000 in 1999 could buy you more than it could 20 years later, in

And having a $1,000 today will theoretically buy you more than having $1,000 five years from now. With that in mind, the time value of money formula can help you determine the present value of the money you have today and how much it could be worth in the future. With investing, however, there is a certain amount of risk you should consider as you use the time value of money. For example, saying you’ll take that $1,000 and invest it in your favorite company that’s expected to provide a 5% return each year is not guaranteed. Instead, with this any investment, you’re accepting the risk of losing money for the chance to beat inflation and increase the future value of your money. Why Is the Time Value of Money Important? The time value of money is important because it allows investors to make a more informed decision about what to do with their money. The TVM can help you understand which option may be best based on interest, inflation, risk and return. It can also be used to help you understand how much money to save in an account if you have a certain goal in mind, such as saving $20,000 in five years if the account earns 3 percent compound interest each year. The Importance of Compounding Interest If the basic idea of the TVM is that money is worth more today than it is tomorrow, you’d think it’d be wiser to spend it now rather than save it for later - but we know that isn’t always the case. While inflation works against you, meaning it makes your dollar worth less tomorrow than today, compound interest can work in your favor to elevate the value of your present dollar tomorrow. With compounding interest, the amount of money you’re earning interest on grows in each compounding period. For example, if you have $1,000 and it earns 10% compounding interest every year for five years, the compounding period would be one year. While that means in the first you’ve earned $100 in interest (10% of $1,000), in that second year you’re actually earning interest on the total amount from the previous compounding period, which would be $1,100 (the original $1, plus the $110 in interest earned in year one). By the end of year two, you’d have earned $1, ($1,100 plus $110 in interest). If you keep going until the end of year five, you would have turned that $1,000 into approximately $1,610. If we consider that the highest inflation rate over the last 10 years was three percent, then in this scenario, choosing to invest your present money using

compounding interest leaves you with a favorable and profitable outcome when compared to not investing it at all.^1 The Time Value of Money Formula The following make up the components of the TVM:  PV: present value  FV: future value  R: rate of growth or interest rate  N: number of periods (typically measured in years or months) Using those values, this is the time value of money formula: FV = PV x (1+I)^N Or, if you’d like to understand the present value of future earnings, you could use: PV = FV / (1+I)^N As we mentioned before, these formulas can be used in different circumstances to help investors or savers understand the value of money today in relation to its earning potential in the future. The TVM is an important piece of understanding the affect inflation has on our money and why investing early can help increase the value of your dollar by giving it time to grow and beat inflation rates. What Is Compounding? Compounding is the process in which an asset's earnings, from either capital gains or interest, are reinvested to generate additional earnings over time. This growth, calculated using exponential functions, occurs because the investment will generate earnings from both its initial principal and the accumulated earnings from preceding periods. Compounding, therefore, differs from linear growth, where only the principal earns interest each period. Understanding Compounding Compounding typically refers to the increasing value of an asset due to the interest earned on both a principal and accumulated interest. This phenomenon, which is a direct realization of the time value of money (TMV) concept, is also known as compound interest. Compound interest works on both assets and liabilities. While compounding boosts the value of an asset more rapidly, it can also increase the amount of money owed on a loan, as interest accumulates on the unpaid principal and previous interest charges. To illustrate how compounding works, suppose $10,000 is held in an account that pays 5% interest annually. After the first year or compounding period, the total in the account has risen to $10,500, a simple reflection of $500 in interest being added to the $10,000 principal. In year two, the account realizes 5% growth on both the original principal and the $500 of first-year interest, resulting in a second-year gain of $525 and a balance of $11,025. After 10 years, assuming no withdrawals and a steady 5% interest rate, the account would grow to $16,288.95. Special Considerations

Compounding is a compelling concept, and no wonder Albert Einstein called it the 8 th^ wonder of the world. Under compounding, you can make your money work harder for you. The interest that accumulates earns more interest in the long term. Also, the longer you stay invested, the higher will be the return from an investment. Hence it is advisable to start investing at early ages to benefit from the power of compounding. What Is the Rule of 72? The Rule of 72 is a quick, useful formula that is popularly used to estimate the number of years required to double the invested money at a given annual rate of return. While calculators and spreadsheet programs like Microsoft's Excel have inbuilt functions to accurately calculate the precise time required to double the invested money, the Rule of 72 comes in handy for mental calculations to quickly gauge an approximate value. Alternatively, it can compute the annual rate of compounded return from an investment given how many years it will take to double the investment. How to Use the Rule of 72 The Rule of 72 could apply to anything that grows at a compounded rate, such as population, macroeconomic numbers, charges, or loans. If the gross domestic product (GDP) grows at 4% annually, the economy will be expected to double in 72 / 4 = 18 years. With regards to the fee that eats into investment gains, the Rule of 72 can be used to demonstrate the long-term effects of these costs. A mutual fund that charges 3% in annual expense fees will reduce the investment principal to half in around 24 years. A borrower who pays 12% interest on their credit card (or any other form of loan that is charging compound interest) will double the amount they owe in six years. The rule can also be used to find the amount of time it takes for money's value to halve due to inflation. If inflation is 6%, then a given purchasing power of the money will be worth half in

around 12 years (72 / 6 = 12). If inflation decreases from 6% to 4%, an investment will be expected to lose half its value in 18 years, instead of 12 years. Additionally, the Rule of 72 can be applied across all kinds of durations provided the rate of return is compounded annually. If the interest per quarter is 4% (but interest is only compounded annually), then it will take (72 / 4) = 18 quarters or 4.5 years to double the principal. If the population of a nation increases at the rate of 1% per month, it will double in 72 months, or six years. Types of interest rates Nominal Interest Rate The nominal interest rate is the stated interest rate of a bond or loan, which signifies the actual monetary price borrowers pay lenders to use their money. If the nominal rate on a loan is 5%, borrowers can expect to pay $5 of interest for every $100 loaned to them. This is often referred to as the coupon rate because it was traditionally stamped on the coupons redeemed by bondholders. Real Interest Rate The real interest rate is so named, because unlike the nominal rate, it factors inflation into the equation, to give investors a more accurate measure of their buying power, after they redeem their positions. If an annually compounding bond lists a 6% nominal yield and the inflation rate is 4%, then the real rate of interest is actually only 2%. Special Considerations It’s feasible for real interest rates to be in negative territory if the inflation rate exceeds the nominal rate of an investment. For example, a bond with a 3% nominal rate will have a real interest rate of - 1%, if the inflation rate is 4%. A comparison of real and nominal interest rates can be calculated using this equation: Effective Interest Rate Investors and borrowers should also be aware of the effective interest rate, which takes the concept of compounding into account. For example, if a bond pays 6% annually and compounds semiannually, an investor who places $1,000 in this bond will receive $30 of interest payments after the first 6 months ($1,000 x .03), and $30.90 of interest after the next six months ($1,030 x .03). In total, this investor receives $60.90 for the year. In this scenario, while the nominal rate is 6%, the effective rate is 6.09%.

EIR =( 1 + i )

Mayank and Vivek are brothers. Mayank is 25 years old and starts a Systematic Investment Plan (SIP) of Rs 5,000 per month in a mutual fund, with growth option (which means returns will be reinvested for compounding to work). SIP essentially means that he does not need to have a large sum to invest in a mutual fund. He can instead break it into monthly regular parts for his investment. Meanwhile, 30-year-old Vivek also starts the same SIP with Mayank. They both want to keep investing till they retire at 60 years. Assuming they got an average return of 9% each year when they both turn 60, Mayank's accumulated amount would have reached Rs1.35 crore and Vivek's amount will be Rs 85.7 lakh rupees. So by starting just five years earlier, Mayank will get Rs 49.9 lakh more than Vivek! This simple example shows that if you start early, invest regularly and avoid withdrawing from this accumulating amount, your investment will grow manifold. This will enable you to create wealth and fulfil your financial goals in life like buying that dream house, funding your child's education or your own retirement in a much easier way.

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EIR =( 1 + i )