document.write( "Question 178354: You have $500 in your savings account. Suppose you have a choice of keeping your money for five years in a savings account with a 2% interest rate, or in a five year certificate of deposit with and interest rate of 4.5%. Calculate how much interest you would earn with each option over five years time with continuous compounding. \n" ); document.write( "

Algebra.Com's Answer #133372 by EMStelley(208) $\"\"$ $\"About$

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The first thing we need to know for this problem is the formula for continuous compounding. With an initial amount (principal) of P, a rate r, and a time t, the amount is
\n" ); document.write( " $\"A=Pe%5E%28rt%29\"$
\n" ); document.write( "So for our first situation, P=500, r=0.02, and t=5. So the amount in the account after 5 years would be
\n" ); document.write( " $\"A=500e%5E%280.02%2A5%29=552.59\"$
\n" ); document.write( "So the amount of interest would be 552.59-500=$52.59.
\n" ); document.write( "For the second situation, P=500, r=0.045 and t=5.
\n" ); document.write( " $\"A=500e%5E%280.045%2A5%29=626.16\"$
\n" ); document.write( "So the amount of interest would be 626.16-500=$126.16. \n" ); document.write( "

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