Answer :
Let's solve question 7:
We want to calculate how much [tex]$25,000 would earn in one hour if the interest rate is 5% compounded hourly. To find the interest compounded hourly, we will use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial amount of money). - \( r \) is the annual interest rate (in decimal form, so 5% becomes 0.05). - \( n \) is the number of times that interest is compounded per year. - \( t \) is the time the money is invested for, in years. Since we're looking for the amount earned in one hour, we have: - Principal \( P = $[/tex]25,000 \)
- Annual interest rate [tex]\( r = 5\% \)[/tex] or [tex]\( 0.05 \)[/tex] as a decimal.
- [tex]\( n = 365 \times 24 \)[/tex] (since interest is compounded hourly, there are 24 hours in a day and 365 days in a year).
Now, we need to express the time [tex]\( t \)[/tex] in years for the formula to work correctly. Since we are only interested in the interest after one hour, [tex]\( t \)[/tex] will be [tex]\(\frac{1}{365 \times 24}\)[/tex] of a year.
Let's apply all this information to the formula:
[tex]\[ A = 25000 \left(1 + \frac{0.05}{365 \times 24}\right)^{365 \times 24 \times \frac{1}{365 \times 24}} \][/tex]
[tex]\[ A = 25000 \left(1 + \frac{0.05}{8760}\right)^1 \][/tex]
[tex]\[ A = 25000 \left(1 + 0.00000571\right) \][/tex]
[tex]\[ A ≈ 25000 \times 1.00000571 \][/tex]
[tex]\[ A ≈ 25000 + 25000 \times 0.00000571 \][/tex]
[tex]\[ A ≈ 25000 + 0.14275 \][/tex]
[tex]\[ A ≈ 25000.14275 \][/tex]
The total amount after one hour will be approximately [tex]$25000.14275. Now to find out how much was earned in that one hour, we subtract the principal from the total amount after compounding: \[ \text{Earned Interest} = A - P \] \[ \text{Earned Interest} ≈ 25000.14275 - 25000 \] \[ \text{Earned Interest} ≈ 0.14275 \] So, $[/tex]25,000 would earn approximately $0.14275 in one hour at an interest rate of 5% compounded hourly.
As for question 8, the continuation of the question was cut off, so we're unable to solve that one. If you would like to provide the full question for question 8, I would be happy to assist you with the solution.
We want to calculate how much [tex]$25,000 would earn in one hour if the interest rate is 5% compounded hourly. To find the interest compounded hourly, we will use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial amount of money). - \( r \) is the annual interest rate (in decimal form, so 5% becomes 0.05). - \( n \) is the number of times that interest is compounded per year. - \( t \) is the time the money is invested for, in years. Since we're looking for the amount earned in one hour, we have: - Principal \( P = $[/tex]25,000 \)
- Annual interest rate [tex]\( r = 5\% \)[/tex] or [tex]\( 0.05 \)[/tex] as a decimal.
- [tex]\( n = 365 \times 24 \)[/tex] (since interest is compounded hourly, there are 24 hours in a day and 365 days in a year).
Now, we need to express the time [tex]\( t \)[/tex] in years for the formula to work correctly. Since we are only interested in the interest after one hour, [tex]\( t \)[/tex] will be [tex]\(\frac{1}{365 \times 24}\)[/tex] of a year.
Let's apply all this information to the formula:
[tex]\[ A = 25000 \left(1 + \frac{0.05}{365 \times 24}\right)^{365 \times 24 \times \frac{1}{365 \times 24}} \][/tex]
[tex]\[ A = 25000 \left(1 + \frac{0.05}{8760}\right)^1 \][/tex]
[tex]\[ A = 25000 \left(1 + 0.00000571\right) \][/tex]
[tex]\[ A ≈ 25000 \times 1.00000571 \][/tex]
[tex]\[ A ≈ 25000 + 25000 \times 0.00000571 \][/tex]
[tex]\[ A ≈ 25000 + 0.14275 \][/tex]
[tex]\[ A ≈ 25000.14275 \][/tex]
The total amount after one hour will be approximately [tex]$25000.14275. Now to find out how much was earned in that one hour, we subtract the principal from the total amount after compounding: \[ \text{Earned Interest} = A - P \] \[ \text{Earned Interest} ≈ 25000.14275 - 25000 \] \[ \text{Earned Interest} ≈ 0.14275 \] So, $[/tex]25,000 would earn approximately $0.14275 in one hour at an interest rate of 5% compounded hourly.
As for question 8, the continuation of the question was cut off, so we're unable to solve that one. If you would like to provide the full question for question 8, I would be happy to assist you with the solution.
