Question

Levi invested $8,500 in an account paying an interest rate of 3.4% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 18 years?

Answer 1

Using the continuous compound interest formula A = Pe^(rt), with P = $8,500, r = 3.4%, and t = 18 years, Levi would have approximately $15,680 in his account after 18 years.

Step-by-step explanation:

To find out how much money Levi would have in the account after 18 years, we need to use the formula for continuous compound interest, which is A = Pert, where A is the amount of money accumulated after n years, including interest, P is the principal amount ($8,500), r is the annual interest rate (as a decimal, so 3.4% would be 0.034), t is the time the money is invested for, and e is the base of the natural logarithm (approximately 2.71828).

In this case, the formula becomes:

A = 8500 × e(0.034 × 18)

When you calculate that, you get:

A ≈ 8500 × 2.71828(0.612)

A ≈ 8500 × 1.84467

A ≈ $15,679.69

Rounding to the nearest ten dollars, Levi would have approximately $15,680 in his account after 18 years.