Question

If $560 is invested at an interest rate of 9% per year and is compounded continuously, how much will the investment be worth in 5 years?

Use the continuous compound interest formula A = Pert

Answer 1

To calculate the future value of an investment compounded continuously, use the formula A = Pert. In this case, the investment will be worth approximately $877.29 in 5 years.

Step-by-step explanation:

To calculate the future value of an investment compounded continuously, we can use the formula A = Pert, where A is the future value, P is the initial principal, r is the annual interest rate, and t is the time in years. In this case, P = $560, r = 0.09, and t = 5. Plugging these values into the formula, we get:

A = 560e^(0.09⋅5)

A ≈ 560e^0.45

A ≈ 560 ⋅ 1.5662

A ≈ $877.29

Therefore, the investment will be worth approximately $877.29 in 5 years.

Answer 2

$878.25

Step-by-step explanation:

Continuously compounded interest is:

A = Pe^(rt)

where A is the final amount, P is the initial amount, r is the interest rate, and t is the number of compoundings.

Here, P = 560, r = 0.09, and t = 5.

A = 560e^(0.09×5)

A = 878.25