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

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Question
Find the effective rate of interest for an investment that earns 5 1/2% per year, compounded continuously
Options
A. 5.65%
B. 5.75%
C. 5.85%
D. 5.95%

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%