nate deposited $1,000 in an account earning 5% interest compounded annually. to the nearest cent, how much…

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 interest rate to decimal

Given $r = 5%=0.05$, $P=$1000$, and $t = 4$ years.

Step3: Substitute values into the formula

$A=1000\times(1 + 0.05)^4$. First, calculate $(1 + 0.05)^4=(1.05)^4$. $(1.05)^4=1.05\times1.05\times1.05\times1.05 = 1.21550625$. Then, $A = 1000\times1.21550625=$1215.51$ (rounded to the nearest cent).

Answer:

$1215.51$