Question

Stan borrows $5,500 at a rate of 12% interest per year. What is the amount due at the end of 5 years if the interest is compounded continuously? In your final answer, include your calculations. PLEASE EXPLAIN.

Answer 1

To calculate the amount due at the end of 5 years with continuous compound interest, use the formula A = P*e^(rt), where A is the amount due, P is the principal, e is Euler's number, r is the interest rate, and t is the time. In this case, the amount due is approximately $10,021.66.

Step-by-step explanation:

To calculate the amount due at the end of 5 years with continuous compound interest, we can use the formula A = P*e^(rt), where A is the amount due, P is the principal (initial amount borrowed), e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time in years.

In this case, the principal is $5,500, the interest rate is 12% or 0.12, and the time is 5 years.

So, A = $5,500 * e^(0.12 * 5) = $5,500 * e^0.6 ≈ $5,500 * 1.82212 ≈ $10,021.66.

Therefore, the amount due at the end of 5 years with continuous compound interest is approximately $10,021.66.

Answer 2

Without compound interest, Stan would earn only $8,800.00. This means that thanks to the power of compound interest Stan will earn an additional $1,191.83 in interest at the end of the 5-year-term.