Answer:
To calculate the amount owed at the end of year one and year two on a loan of $2500 with an interest rate of 4% compounded annually, we can use the formula for compound interest. The formula is given by:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the loan
P = the principal amount (initial loan amount)
r = annual interest rate (expressed as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, the principal amount (P) is $2500, the annual interest rate (r) is 4% or 0.04, and since the interest is compounded annually, n is equal to 1.
Let's calculate the amount owed at the end of year one:
A1 = 2500(1 + 0.04/1)^(1*1)
A1 = 2500(1 + 0.04)^1
A1 = 2500(1.04)
A1 = $2600
Therefore, at the end of year one, the amount owed on the loan would be $2600.
Now, let's calculate the amount owed at the end of year two:
A2 = 2500(1 + 0.04/1)^(1*2)
A2 = 2500(1 + 0.04)^2
A2 = 2500(1.04)^2
A2 ≈ $2704.16
Therefore, at the end of year two, the amount owed on the loan would be approximately $2704.16.
In summary:
- Amount owed at the end of year one: $2600
- Amount owed at the end of year two: approximately $2704.16
Explanation: