Answer:
It will take approximately 6.89 years for the investment to grow to $9737.
Explanation:
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the present value of the investment
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
We know that P = $7000, r = 0.034, n = 4 (since the interest is compounded quarterly), and we want to find t when A = $9737.
$9737 = $7000(1 + 0.034/4)^(4t)
Divide both sides by $7000:
1.391 = (1 + 0.034/4)^(4t)
Take the natural logarithm of both sides:
ln(1.391) = ln[(1 + 0.034/4)^(4t)]
Use the power rule of logarithms:
ln(1.391) = 4t * ln(1 + 0.034/4)
Divide both sides by 4 ln(1 + 0.034/4):
t = ln(1.391) / [4 * ln(1 + 0.034/4)]
Using a calculator, we find:
t ≈ 6.89 years
Therefore, it will take approximately 6.89 years for the investment to grow to $9737.