what is the rate compounded every 3 months that will make $4770 become $8233 in 3 years ?
4770(1+r/4)^(4*3) = 8233
(1+r/4)^12 = 1.726
1+r/4 = 1.0465
r/4 = .0465
r = .186 = 18.6%
UUHH...OH
To find the rate compounded every 3 months that will make $4770 become $8233 in 3 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount ($8233)
P = Principal amount ($4770)
r = Annual interest rate (unknown)
n = Number of times interest is compounded per year (12 months divided by 3 months = 4)
t = Time in years (3 years)
Rearranging the formula, we can solve for r:
r = ([(A / P)^(1 / (n*t)]) - 1) * n
Now let's substitute the given values into the formula:
r = ([(8233 / 4770)^(1 / (4*3)]) - 1) * 4
Simplifying this equation step by step:
r = (1.72414505^0.083333333) - 1) * 4
r = (1.08107816 - 1) * 4
r = 0.08107816 * 4
r ≈ 0.32431264
Therefore, the approximate interest rate per quarter that will make $4770 become $8233 in 3 years is 0.3243 or 32.43%.