In an investment environment, an initial outlay of $100 grows to $156 in 7 years. The quarterly compounded rate of annual interest implicit in this is:
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A. B. C. D.B
There are 28 quarters in 7 years. If the quarterly compounded rate is r, then we have 100*(1+r/4)^28 = 156, giving r = 6.4%
To determine the quarterly compounded rate of annual interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where: A = Final amount (in this case, $156) P = Principal or initial outlay (in this case, $100) r = Annual interest rate n = Number of times interest is compounded per year (quarterly in this case) t = Number of years (in this case, 7)
We need to solve for r.
Rearranging the formula, we get:
r = ([(A/P)^(1/nt)] - 1) * n
Plugging in the given values:
A = $156 P = $100 n = 4 (quarterly compounding) t = 7
r = ([(156/100)^(1/(4*7))] - 1) * 4 = ([1.56^(1/28)] - 1) * 4 ≈ (1.023424 - 1) * 4 ≈ 0.023424 * 4 ≈ 0.093696
To convert this decimal rate to a percentage, we multiply by 100:
r ≈ 0.093696 * 100 ≈ 9.3696%
Therefore, the quarterly compounded rate of annual interest implicit in this investment is approximately 9.3696%.
None of the provided answer choices exactly match this value. However, the closest option is option B, which states 6.40%. Please note that there may be a discrepancy between the given answer choices and the actual calculated value.