Final answer:
The interest on a 9-year loan for $18,611 at an annual rate of 4.2% with continuous compounding is approximately $8,552, rounded to the nearest dollar.
Step-by-step explanation:
To compute the interest on a loan with continuous compounding, you can use the formula A = Pert, where P is the principal amount ($18,611), r is the annual interest rate (4.2% or 0.042 as a decimal), and t is the time in years (9 years).
First, let's calculate the total amount A after 9 years of continuous compounding:
A = 18611e(0.042 × 9)
Using a calculator:
A = 18611 × e(0.378)
A = 18611 × 1.4596
A ≈ 27163
The total amount after 9 years is approximately $27,163. To find the total compound interest, we subtract the principal from this total:
Interest = A - P
Interest = 27163 - 18611
Interest ≈ 8552
Therefore, the interest accrued on the loan after 9 years is about $8,552, rounded to the nearest dollar.