Question

Elisa deposits $200 in an account that earns 3% interest compounded annually. She wants to know how many years it will take for the amount in her account to double. Write an equation to model this situation, where "t" is the number of years it will take for the amount in the account to double.

a. 200(1 + 0.03)^t = 400
b. 200(1 - 0.03)^t = 400
c. 200(1 + 0.03)^(2t) = 400
d. 200(1 - 0.03)^(2t) = 400

Answer 1

The correct model to represent the situation where the principal amount of $200 at an annual compounded interest rate of 3% grows to double its amount is: 200(1 + 0.03)^t = 400.

Step-by-step explanation:

To find out how many years it will take for an account balance to double given a certain interest rate, we use the formula A = P(1 + r)^t, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), and t is the time in years. Here, Elisa wants her $200 to double, so we aim to solve for t when the accumulated amount A is $400. Given that the interest rate is 3% or 0.03, the formula becomes:

400 = 200(1 + 0.03)^t

This can be simplified to the equation:

200(1 + 0.03)^t = 400

Therefore, the correct model to represent the situation where "t" stands for the number of years it'll take for the money to double is:

a. 200(1 + 0.03)^t = 400