Question

albert has $1,000 in an account. the interest rate is 5% compounded annually. to the nearest cent, how much interest will he earn in 4 years? $

Explanation:

Step1: Recall 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 time the money is invested for in years. First, we need to find the amount $A$ after 4 years and then subtract the principal $P$ to find the interest earned.

Step2: Convert the interest rate to decimal

The interest rate $r$ is 5%, which in decimal form is $r=\frac{5}{100} = 0.05$.

Step3: Identify the principal and time

The principal $P=\$1000$ and the time $t = 4$ years.

Step4: Calculate the amount $A$

Substitute the values into the compound interest formula: $A=1000(1 + 0.05)^4$. First, calculate $(1 + 0.05)^4=(1.05)^4$. We know that $1.05^4=1.05\times1.05\times1.05\times1.05 = 1.21550625$. Then, $A = 1000\times1.21550625=\$1215.50625$.

Step5: Calculate the interest earned

The interest earned $I$ is the amount $A$ minus the principal $P$. So, $I=A - P=1215.50625-1000 = 215.50625$. Rounding to the nearest cent (two decimal places), we get $I=\$215.51$.

Answer:

$\$215.51$