sam has $50 in an account that earns 5% interest compounded annually. to the nearest cent, how much will he…

Explanation:

Step1: Identify the 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 $r = 5%=\frac{5}{100}=0.05$, $P = 50$, and $t = 3$.

Step3: Substitute the values into the formula

$A=50\times(1 + 0.05)^3$. First, calculate $(1 + 0.05)^3=(1.05)^3=1.05\times1.05\times1.05 = 1.157625$. Then, $A = 50\times1.157625=57.88125$.

Step4: Round to the nearest cent

Rounding $57.88125$ to the nearest cent gives $57.88$.

Answer:

$57.88$