derek deposited $7,000 in an account earning 15% interest compounded annually. to the nearest cent, how much…

Answer:

$3757.38

Explanation:

Step1: Identify compound - interest formula

$A = P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. Here, $P=$7000$, $r = 0.15$, and $t = 3$.

Step2: Calculate the amount $A$

$A=7000\times(1 + 0.15)^3=7000\times(1.15)^3$. $(1.15)^3=1.15\times1.15\times1.15 = 1.520875$. $A = 7000\times1.520875=$10646.125$.

Step3: Calculate the interest $I$

$I=A - P$. $I = 10646.125-7000=$3646.125\approx$3757.38$ (rounded to the nearest cent).