In the equation A = B e k t where B is the initial amount and t is the time taken what is k,I know it's a constant of proportionality ,but is it the same as the number of time a certain amount of money gets compounded every year?For example, if an amount of $ 500 is getting compounded four times at the rate of 5 % per year ,here if they ask what is the amount if the money is compounded every instant ,the equation will the somewhat similar to exponential growth equation,is the number 4 here same as k?

Question

In the equation  A  =  B      e          k      t      where B is the initial amount and t is the time taken what is k,I know it&#039;s a constant of proportionality ,but is it the same as the number of time a certain amount of money gets compounded every year?For example, if an amount of $ 500 is getting compounded four times at the rate of 5 % per year ,here if they ask what is the amount if the money is compounded every instant ,the equation will the somewhat similar to exponential growth equation,is the number 4 here same as k?

Yaritza Cardenas · Accepted Answer

If we took your example of $500 compounded four times at the rate of 5% per year and wrote it as   A  =  500  ×  (  1.05      )    4    ≈  607.75 then we could write this as   A  =  B      e          k      t       whereB=500, the initial amountt=4, the time in years  k  =      log    e    ⁡  (  1.05  )  ≈  0.04879and get the same result. The same approach would work for integer t, and we could see it as a reasonable approach for non-integer time t.To me in this example       e    k    −  1  =  0.05 is the annual rate of growth, but some people use that phrase to mean k itself and so it is important that two people communicating are clear about what they are talking about.

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