An investment of $2,300 grows to $2,904 in 4 years. The annually compounded rate of return is:
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A. B. C. D.A
Let r be the annually compounded rate. Then, 2904 = 2300*(1+r)^4. Hence, r = (2904/2300)^(1/4) - 1 = 6%
To find the annually compounded rate of return, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where: A = the future value of the investment ($2,904) P = the initial investment ($2,300) r = the annual interest rate (what we need to find) n = the number of times the interest is compounded per year (since it's annually compounded, n = 1) t = the number of years (4 years)
We need to rearrange the formula to solve for r:
r = (A/P)^(1/(nt)) - 1
Plugging in the given values:
r = (2,904/2,300)^(1/(1*4)) - 1
Simplifying:
r = 1.26^(1/4) - 1
Calculating the exponent:
r = 1.0625 - 1
r = 0.0625
To convert the rate to a percentage, we multiply by 100:
r = 0.0625 * 100
r = 6.25%
Therefore, the annually compounded rate of return is 6.25%. The correct answer is B. 6.25%.