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Time Value of Money Introduction
In essence, time value of money refers to the growth of 1 dollar as time increases. 1 dollar today is worth more 10 years down the road because it can earn interest payments. How much is 1$ worth 10 years down the road? This answer depends on various factors such as the interest rate, monthly/quarterly/annual compounding, payment contributions or withdrawals and more. Here is some basic terminology of the time value of money function: Future Value - Refers to how much an investment grows over a certain period of time. Example $5000 invested today grows to over $29,010 in 5 years of time with an interest rate of 5% compounded annually. Present Value - Refers to how much an investment is worth today. Therefore from the example above, if i invest $5000 today, the Present Value (PV) is $5000. The future value in 5 years is $29,010. Compounding Interest - This is the process of accumulating interest earnings in an investment over time, to further increase the interest earnings. Here's a simple example: - You invest $100 today into a savings account earning you 10% interest rate compounded annually. - At the end of Year 1, you'd have $100 + ($100 * 10%) = $100 + $10 = $110 - At the beginning of Year 2, the total you have accumulated thus far is $110. - At the end of Year 2, you'd have $110 + ($110 * 10%) = $110 + $11 = $121 - At the beginning of Year 3, the total you would have accumulated thus far is $121. - At the end of Year 3, you'd have $121 + ($121 * 10%) = $121 + $12.1 = $133.1 In a matter of 3 years, you were able to grow $100 to $133.1 with 10% interest compounded annually. This is the power of compound interest !! Imagine if you had initially invested $100,000 into the same account. In 3 years, the total amount it would grow to is $133,100. Therefore, you earned $33,100 in 3 years thanks to compound interest!! Formula for Future Value The formula for future value is Future Value = $1 x (1 + r)t where r stands for the interest rate, and t stands for the # of years. To confirm the above answers we got for the $100 invested today, we have: 2 years= $100 x (1+0.1)2 = $121 Here's a table below to summarize these calculations:
Graphical Representation of Compound Interest
Notice the column "Simple Interest." Simple Interest is simply $100 x 0.1 = $10. Since simple interest is NOT compounded, you will always earn a flat rate of $10 generated by the 10% Homework Question: If you have $200 to invest now, how much will it be worth in 5 years with an interest rate of 5% compounded annually? Answer: $200 x (1+0.05)5 = $255.25
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