Question

You deposit $1500 into an account that pays an interest rate of 4% compounded annually. What is the balance after 5 years? Your friend deposits $1500 into an account that pays a simple annual interest rate of 4%. What is the balance after 5 years?

Answer 1

Compound interest: A = $1824.98

Simple interest: A = $1800

Step-by-step explanation:

To know the balance after t years for an account that pays with a compounded rate, we can use the following equation:

`A=P(1+r)^t`

Where P is the initial amount and r is the interest rate.

So, replacing P by $1500, r by 4% or 0.04, and t by 5 years, we get:

`\begin{gathered} A=1500(1+0.04)^5 \\ A=1500(1.04)^5 \\ A=1824.98 \end{gathered}`

Therefore, in this case, the balance after 5 years is $1824.98

On the other hand, the balance after t years for an account that pays with a simple interest rate can be calculated as:

`A=P(1+rt)`

So, replacing P by $1500, r by 0.04, and t by 5 years, we get:

`\begin{gathered} A=1500(1+0.04\cdot5) \\ A=1500(1+0.2) \\ A=1500(1.2) \\ A=1800 \end{gathered}`

Then, the balance after 5 years is $1800

So, the answers are:

Compound interest: A = $1824.98

Simple interest: A = $1800