Question

josiah invests $5000 into an account that accrues 3% interest annually. assuming no deposits or withdrawals are made, which equation represents the amount of money in josiah’s account, y, after x years?

• $y = 5000(1.3)^x$
• $y = 5000(0.3)^x$
• $y = 5000(1.03)^x$
• $y = 5000(0.03)^x$

Explanation:

Step1: Recall compound interest formula

The formula for annual compound interest (with no additional deposits/withdrawals) is $y = P(1 + r)^x$, where $P$ is principal, $r$ is annual interest rate, $x$ is time in years, and $y$ is final amount.

Step2: Identify given values

Principal $P = 3850$, annual interest rate $r = 2\% = 0.02$.

Step3: Substitute values into formula

$y = 3850(1 + 0.02)^x = 3850(1.02)^x$

Answer:

$y = 3850(1.02)^x$ (matches the first option listed)