Answer:
it will take approximately 9.08 years for Tanisha's investment to grow from $1,000 to $1,800 at a 6% interest rate compounded semiannually.
Explanation:
1. Rewrite the formula using the given values:
$1,800 = $1,000 * (1 + (0.06 / 2))^(2 * t)
2. Simplify the formula:
1.8 = (1.03)^(2t)
3. Take the natural logarithm of both sides of the equation to isolate the exponent:
ln(1.8) = ln((1.03)^(2t))
4. Use the property of logarithms to bring down the exponent:
ln(1.8) = 2t * ln(1.03)
5. Divide both sides of the equation by 2ln(1.03):
t = ln(1.8) / (2 * ln(1.03))
6. Use a calculator to find the approximate value of t:
t ≈ 9.08 years