Develop an amortization schedule for the loan described. (Round your answers to the nearest cent.) $\$ 150,000$ for 3 years at $6 \%$ compounded annually
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Step 1 ：The problem is asking for an amortization schedule for a loan of $150,000 for 3 years at an annual interest rate of 6% compounded annually. An amortization schedule is a complete table of periodic loan payments, showing the amount of principal and the amount of interest that comprise each payment until the loan is paid off at the end of its term.

Step 2 ：To solve this problem, we need to calculate the annual payment first. The formula for the annual payment (A) of a loan is given by: \(A = P * r * (1 + r)^n / ((1 + r)^n - 1)\) where: P = principal amount (the initial amount of loan), r = annual interest rate (in decimal), n = number of years.

Step 3 ：After calculating the annual payment, we can then calculate the interest and principal portions of each payment for each year. The interest for a given year is calculated by multiplying the remaining balance of the loan by the interest rate. The principal portion of the payment is then the total payment minus the interest.

Step 4 ：The annual payment is approximately \$56116.47. The remaining balance after 3 years is approximately \$0.00, which is expected as the loan should be fully paid off after 3 years.

Step 5 ：\(\boxed{\text{Final Answer: The amortization schedule for the loan is as follows:}}\)

Step 6 ：Year 1: Payment = \$56116.47, Interest = \$9000.00, Principal = \$47116.47, Remaining balance = \$102883.53

Step 7 ：Year 2: Payment = \$56116.47, Interest = \$6173.01, Principal = \$49943.46, Remaining balance = \$52940.07

Step 8 ：Year 3: Payment = \$56116.47, Interest = \$3176.40, Principal = \$52940.07, Remaining balance = \$0.00

Step 9 ：This means that the borrower will need to make annual payments of approximately \$56116.47 for 3 years to fully pay off the loan. The interest portion of the payment decreases each year, while the principal portion increases.