Answer: $30 in six years at an interest rate of 5% is $4,574.36.
Explanation:
We can use the formula for compound interest to solve this problem. The formula is:
A = P(1 + r/n)^(nt)
where A is the amount of money at the end of the time period, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
We know that the interest rate is 5%, and the time period is 6 years. We also know that we want to earn $30 in interest. Therefore, we can set up the following equation:
A = P(1 + r/n)^(nt)
A - P = 30
r = 0.05
t = 6
We don't know the value of P, so we need to solve for it. We can simplify the equation by substituting in the values we know:
A = P(1 + r/n)^(nt)
A = P(1 + 0.05/1)^(1*6)
A = P(1.05)^6
Now we can substitute this expression for A into the equation we set up earlier:
A - P = 30
P(1.05)^6 - P = 30
We can factor out the P on the left-hand side:
P[(1.05)^6 - 1] = 30
Now we can solve for P by dividing both sides by [(1.05)^6 - 1]:
P = 30 / [(1.05)^6 - 1]
Using a calculator, we get:
P = $4,574.36
Therefore, the principal that must be invested to earn $30 in six years at an interest rate of 5% is $4,574.36.