Question

You put $500 in an account that earns 4% annual interest. The interest earned each year is added to the principal to create a new principal. Find the total amount in your account after each year for 3 years.

Answer 1

To find the total amount in your account after each year for 3 years, you can use the formula for compound interest.

Step-by-step explanation:

To find the total amount in your account after each year for 3 years, you can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the total amount, P is the principal, r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years. In this case, P = $500, r = 0.04 (4% as a decimal), n = 1 (since it's compounded annually), and t = 3. Plugging these values into the formula, we get:

A = $500(1 + 0.04/1)^(1*3)

A = $500(1.04)^3

A = $500(1.124864)

A = $562.43

So, the total amount in your account after each year for 3 years will be approximately $562.43.

Answer 2

`\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$500\\ r=rate\to 4\%\to (4)/(100)\to &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{APR, so it's annual, once} \end{array}\to &1\\ t=years\to &3 \end{cases} \\\\\\ A=500\left( 1+(0.04)/(1) \right)^(1\cdot 3)`