Answer :
To determine how much Robert will pay Steve at the end of 163 days, we need to calculate the simple interest earned during this period and then find the total amount to be paid.
Here’s how to solve the problem step by step:
1. Identify the Principal Amount:
The principal amount loaned by Steve to Robert is [tex]$10,280.
2. Determine the Interest Rate:
The annual interest rate is 10%.
3. Specify the Time Period:
The loan duration is 163 days.
4. Assume 365 days in a year:
For calculating interest, we use 365 days as the number of days in a year.
5. Calculate the Simple Interest:
The formula for simple interest is:
\[
\text{Simple Interest} = \text{Principal} \times \text{Rate} \times \left(\frac{\text{Time in days}}{\text{Days in a year}}\right)
\]
Substituting the known values, we get:
\[
\text{Simple Interest} = 10,280 \times 0.10 \times \left(\frac{163}{365}\right)
\]
Calculating this gives an interest amount of approximately $[/tex]459.08.
6. Calculate Total Payment:
To find out the total amount Robert will have to pay at the end of the loan period, we add the interest to the principal:
[tex]\[
\text{Total Payment} = \text{Principal} + \text{Simple Interest}
\][/tex]
[tex]\[
\text{Total Payment} = 10,280 + 459.08
\][/tex]
This results in a total payment of approximately [tex]$10,739.08.
Hence, at the end of 163 days, Robert will pay Steve $[/tex]10,739.08. This value is rounded to the nearest cent.
Here’s how to solve the problem step by step:
1. Identify the Principal Amount:
The principal amount loaned by Steve to Robert is [tex]$10,280.
2. Determine the Interest Rate:
The annual interest rate is 10%.
3. Specify the Time Period:
The loan duration is 163 days.
4. Assume 365 days in a year:
For calculating interest, we use 365 days as the number of days in a year.
5. Calculate the Simple Interest:
The formula for simple interest is:
\[
\text{Simple Interest} = \text{Principal} \times \text{Rate} \times \left(\frac{\text{Time in days}}{\text{Days in a year}}\right)
\]
Substituting the known values, we get:
\[
\text{Simple Interest} = 10,280 \times 0.10 \times \left(\frac{163}{365}\right)
\]
Calculating this gives an interest amount of approximately $[/tex]459.08.
6. Calculate Total Payment:
To find out the total amount Robert will have to pay at the end of the loan period, we add the interest to the principal:
[tex]\[
\text{Total Payment} = \text{Principal} + \text{Simple Interest}
\][/tex]
[tex]\[
\text{Total Payment} = 10,280 + 459.08
\][/tex]
This results in a total payment of approximately [tex]$10,739.08.
Hence, at the end of 163 days, Robert will pay Steve $[/tex]10,739.08. This value is rounded to the nearest cent.
