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Compute the interest on a 9-year loan for $18,611 if the annual

rate is 4.2% with continuous compounding. Round your answer to then
nearest dollar.

User Jvliwanag
by
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1 Answer

4 votes

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.

User Ryan Arief
by
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