Final answer:
The principal portion of the total payment in year 4 for a 4-year constant payment loan (CPL) is $3,568.
Step-by-step explanation:
To calculate the principal portion of the total payment in year 4 for a 4-year constant payment loan (CPL), we need to use the amortization formula:
Principal Portion = Total Payment - Interest Portion
The total payment can be calculated using the loan amount, interest rate, and loan term. In this case:
Loan Amount = $11,000
Annual Interest Rate = 11%
Loan Term = 4 years
Using the formula for calculating total payments:
Total Payment = (Loan Amount / Number of Payments) + (Loan Amount * Interest Rate)
Substituting the given values:
Total Payment = ($11,000 / 4) + ($11,000 * 0.11)
Total Payment = $2,750 + $1,210
Total Payment = $3,960
The interest portion for year 4 can be calculated as:
Interest Portion = Principal Portion * Interest Rate
Since we want to find the principal portion, we rearrange the formula:
Principal Portion = Total Payment - Interest Portion
Substituting the values:
Principal Portion = $3,960 - (Principal Portion * 0.11)
Simplifying the equation:
Principal Portion + 0.11 * Principal Portion = $3,960
Principal Portion * (1 + 0.11) = $3,960
Principal Portion * 1.11 = $3,960
Principal Portion = $3,960 / 1.11
Principal Portion = $3,567.57
Rounded to the nearest dollar, the principal portion of the total payment in year 4 is $3,568.