Question 117059: Suppose that 2000.00 is invested at a rate of 6% per year compounded continuously. What is the balance after 1 year? After 2 years Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! The formula for continuous compounding is:
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in which P is the total future value, C is the initial deposit of money, e is the base of the
natural logarithms and is approximately 2.718281828, r is the annual interest rate expressed
as a decimal, and t is the number of years of the investment.
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For this problem you are told that the initial deposit of money is $2000. Substituting
this value for C in the equation results in the equation becoming:
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You are also told that the annual interest rate is 6%. In decimal form this is 0.06. Substitute
this decimal for r in the equation to get:
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Now that we are this far, we can substitute the two values of t that you are asked to
find the future value (P) for. In the first case you are asked to find the future value
of the $2000 initial deposit if it is left in the investment for 1 year. Substitute 1 for
t in the equation and the equation becomes:
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Now it's basically a calculator problem. The exponent is 0.06 times 1 so it just equals 0.06
and the problem is then:
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If you use your calculator to raise e (or 2.718281828) to the exponent 0.06 you find that
it is 1.061836547 and the equation reduces to:
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When rounded off the answer is that using continuous compounding at an annual rate of 6%
a $2000 initial investment will be worth $2123.67 at the end of one year.
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If the $2000 is left on deposit for 2 years, the only thing that changes in the equation is the
value of t. For this calculation, t = 2 and the equation:
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becomes:
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Using your calculator on you should find that it equals 1.127496852 and this reduces
the equation to:
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When rounded off the answer is that using continuous compounding at an annual rate of 6%
a $2000 initial investment will be worth $2254.99 at the end of two years.
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Hope this helps you to understand how to do continuous compounding for an investment.
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