Question

Introduction to compound interestVSuppose Bob places $7500 in an account that pays 4% interest compounded each year.Assume that no withdrawals are made from the account.Follow the instructions below. Do not do any rounding.(a) Find the amount in the account at the end of 1 year.$0(b) Find the amount in the account at the end of 2 years I need help with this math problem.

Answer 1

The given information is:

- Bob places $7500 in the account

- It pays 4% interest compounded each year

- No withdrawals are made from the account

Part A. Find the amount in the account at the end of 1 year:

So, at the end of the first year, Bob will have in the account the money he placed there plus the money he earned from the 4% interest.

The money from interest is given by:

`\begin{gathered} I=P*r \\ \text{ Where I is the money he earned, P is the principal and r the interest rate} \\ I=7500*0.04=300 \end{gathered}`

Therefore, the amount in the account at the end of 1 year is:

`\begin{gathered} A=P+I \\ A=7500+300 \\ A=7800 \end{gathered}`

Answer: $7800

Part B. Find the amount in the account at the end of 2 years.

So, at the beginning of year 2 Bob has $7800, let's find the interest at the end of year 2:

`I=7800*0.04=312`

At the end of year 2, he will have in the account the following amount:

`\begin{gathered} A=7800+312 \\ A=8112 \end{gathered}`

Answer: $8112