Answer:
IG: yiimbert
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
where:
A = final amount ($600)
P = principal amount ($500)
r = annual interest rate (5% or 0.05 as a decimal)
n = number of times interest is compounded per year (we'll assume it's compounded monthly, so n = 12)
t = time in years
Substituting the given values, we get:
$600 = $500(1 + 0.05/12)^(12t)
Dividing both sides by $500, we get:
1.2 = (1 + 0.05/12)^(12t)
Taking the natural logarithm (ln) of both sides, we get:
ln(1.2) = ln[(1 + 0.05/12)^(12t)]
Using the property of logarithms, we can bring the exponent down:
ln(1.2) = (12t) ln(1 + 0.05/12)
Dividing both sides by 12 ln(1 + 0.05/12), we get:
t = ln(1.2) / [12 ln(1 + 0.05/12)]
Using a calculator, we can evaluate this expression and find that:
t ≈ 2.26 years
Therefore, it will take approximately 2.26 years for the account to reach $600 with an interest rate of 5% and monthly compounding.