Final answer:
To find the ending balance of a $30,000 investment at a 2.5% interest rate compounded hourly for five years, we apply the compound interest formula. By converting the annual rate to the hourly rate and raising this to the total count of compounding hours, multiplied by the principal, we obtain the final amount with compound interest.
Step-by-step explanation:
To calculate the ending balance of a $30,000 investment at a 2.5% interest rate compounded hourly for five years, we use the formula for compound interest: A = P(1 + r/n)^(nt). Where:
- P is the principal amount ($30,000)
- r is the annual interest rate (2.5% or 0.025 as a decimal)
- n is the number of times the interest is compounded per year (hourly compounding means n=24*365)
- t is the number of years the money is invested (t=5).
First, convert the annual interest rate to an hourly rate by dividing by the number of hours in a year, which gives us a rate per hour. Then, raise this rate plus one to the power of the total number of compounding periods (hours in our case), and multiply the result by the initial investment. The calculation will give us the total amount including the power of compound interest after five years.