Suppose Ann places $6000 in an account that pays 4% interest compounded each year.Assume that no withdrawals are made from the account.

1. ### Break Down the Problem

We need to find out how much money Ann will have in her account after a certain number of years, given that she deposits $6000 at an interest rate of 4% compounded annually. The problem can be divided into two parts:

1. Identify the formula for compound interest.
2. Calculate the total amount after a specific number of years.

2. ### Relevant Concepts

The formula for compound interest is given by: $A = P(1 + r)^n$ Where:

• $A$ = the future value of the investment/loan, including interest
• $P$ = the principal investment amount ($6000)
• $r$ = the annual interest rate (decimal) (4% = 0.04)
• $n$ = the number of years the money is invested or borrowed

3. ### Analysis and Detail

Given:

• $P = 6000$
• $r = 0.04$

We need to compute $A$ for a specified number of years; let's say $n = 5$ years as an example:

1. Calculate $(1 + r)$: $1 + r = 1 + 0.04 = 1.04$

2. Compute $(1 + r)^n$: $(1.04)^5 \approx 1.21665 \quad (\text{using a calculator})$

3. Calculate the future value $A$: $A = 6000 \times 1.21665 \approx 7299.90$

4. ### Verify and Summarize

After calculations, Ann will have approximately $7299.90 in her account after 5 years. You can replace $n$ with any number of years to calculate the value for different periods using the same procedure.

Final Answer

After 5 years, Ann will have approximately $7299.90 in her account.