Final answer:
To find the principal that will grow to $3300 in nine years, five months at 5.8% compounded quarterly, we can use the formula for compound interest. Solving the equation will give us the principal value.
Step-by-step explanation:
To find the principal that will grow to $3300 in nine years, five months at 5.8% compounded quarterly, we can use the formula for compound interest:
Compound Interest (A) = P(1 + r/n)^(nt)
Where:
P = principal (unknown)
r = annual interest rate (5.8% or 0.058)
n = number of times interest is compounded per year (quarterly, so n=4)
t = time in years (9 years and 5 months, or approximately 9.42 years)
Now, we can substitute the values into the formula and solve for P:
$3300 = P(1 + 0.058/4)^(4*9.42)
Solving this equation will give us the principal value.