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Find the effective rate of interest for an investment that earns 5 1/2% per year, compounded continuously

Correct Answer: 5.65%

Explanation:


We are not given a value of P in this problem, so either pick a value


for P and stick with that throughout the problem, or just let P = P.


We have that t = 1, and r = .055. To find the effective rate of interest,


first find out how much money we have after one year:


A = Pert


A = Pe(.055)(1)


A = 1.056541P.


Therefore, after 1 year, whatever the principal was, we now have 1.056541P.


Next, find out how much interest was earned, I, by subtracting the initial amount of money from the final amount:


I = A − P


  = 1.056541P − P


  = .056541P.


Finally, to find the effective rate of interest, use the simple interest formula, I = Prt. So,


I = Pr(1) = .056541P


.056541 = r.


Therefore, the effective rate of interest is 5.65%


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