rob has $7,869 in an account that earns 13% interest compounded annually. to the nearest cent, how much will…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1 + r)^t$, 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 (in decimal form), and $t$ is the number of years the money is invested for.

Step2: Convert the percentage to decimal

Given $r = 13%=0.13$, $P = 7869$, and $t = 5$.

Step3: Substitute values into the formula

$A=7869\times(1 + 0.13)^5$. First, calculate $(1 + 0.13)^5=(1.13)^5$. $(1.13)^5=1.13\times1.13\times1.13\times1.13\times1.13 = 1.842435129$. Then, $A = 7869\times1.842435129$. $A=7869\times1.842435129 = 14498.12103$.

Step4: Round to the nearest cent

Rounding $14498.12103$ to the nearest cent gives $A\approx14498.12$.

Answer:

$14498.12$