BTGmoderatorDC wrote:A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16?
A. 16 = 1.02^(x/4)
B. 2 = 1.02^x
C. 16 = 1.08^(4x)
D. 2 = 1.02^(x/4)
E. 1/16 = 1.02^(4x)
When a value increases repeatedly by r%:
Final amount = Original amount * (1 + r/100)^number of changes.
Let original amount = 1.
Since the original amount increases by a factor of 16:
Final amount = 16.
Since the investment increases by 2% every quarter:
r = 2.
Since x = the number of years, and there are 4 changes every year:
Number of changes = 4x.
Plugging these values into the formula:
16 = 1*(1.02)^4x
16^(1/4) = 1.02^(4x*(1/4))
2 = 1.02^x
The correct answer is
B.
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