Answer:
10.2 years
Explanation:
You want to know the number of years it takes an investment of $600 to earn $300 in interest at the rate of 4% compounded quarterly.
Value
After earning $300 interest, the $600 investment will have a value of ...
$300 +600 = $900
Using the given numbers in the given formula, we have ...
A = P(1 +r/n)^(nt)
900 = 600(1 +0.04/4)^(4t)
900/600 = (1 +0.04/4)^(4t)
Taking logarithms, we have ...
log(900/600) = 4t·log(1 +0.04/4)
Dividing by the coefficient of t gives ...
t = log(900/600)/(4·log(1 +0.04/4)) ≈ 10.2
$300 interest will be earned in approximately 10.2 years.
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Additional comment
Of course, we can simplify the expression to ...
t = log(1.5)/(4·log(1.01))
In the attachment, we elected to let the calculator do all the work.
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