To find out how much Adam will pay Susan at the end of 4 years, we need to calculate both the interest accrued and the total amount to be paid back.
Here is the step-by-step solution:
1. Identify the principal amount (P):
The principal amount, or the initial loan amount, is $16,580.
2. Determine the annual interest rate (r):
The interest rate is given as 6%, which can be written in decimal form as 0.06.
3. Establish the time period (t):
The loan period is 4 years.
4. Calculate the interest accrued (I) over the loan period:
The formula to calculate the simple interest is:
[tex]\[
I = P \times r \times t
\][/tex]
Plugging in the values, we get:
[tex]\[
I = 16580 \times 0.06 \times 4 = 3979.2
\][/tex]
So, the interest accrued over 4 years is $3,979.20.
5. Calculate the total amount to be paid (A):
To find the total amount to be paid at the end of the loan period, we add the interest to the principal amount:
[tex]\[
A = P + I
\][/tex]
Combining the principal and the interest, we get:
[tex]\[
A = 16580 + 3979.2 = 20559.2
\][/tex]
So, the total amount Adam will pay Susan at the end of 4 years is $20,559.20.
Hence, after 4 years, Adam will pay Susan $20,559.20.
