Final answer:
To find the total payment at t=3 for the loan, calculate the annual interest, subtract the annual payments, and add the interest for the last year to the remaining balance. After rounding, the total payment at t=3 is $18,846.
Step-by-step explanation:
To calculate the total payment amount at t=3 for a 3-year $19,000 loan with a 7% annual interest rate and equal payments of $2,000 at t=1 and t=2, we need to first determine the interest accumulated after the first and second year and how it affects the remaining balance.
After the first year, the interest is 7% of $19,000, which is $1,330. After paying $2,000, the remaining balance is $18,330. After the second year, 7% interest on $18,330 is $1,283.10. Again, after paying $2,000, the balance becomes $17,613.10.
Now, for the final year, we calculate 7% interest on $17,613.10, which is $1,232.92. Adding this interest to the balance gives us $18,846.02. After rounding to the nearest dollar, the total payment amount at t=3 is $18,846.