Ira invests $8000 into an account that earns 5.6% simple interest for 6 years. He does not make any other deposits or withdrawals.

Question

At the end of 6 years, Ira invests the entire account balance into a different account that earns 6% simple interest. He leaves the money in the account for 3 years without making any additional deposits or withdrawals.

What is the new account balance at the end of 3 years?

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Ira invests $Response area into the account that earns 6% simple interest. At the end of 3 years, the account balance is $Response area.

Answer 1

To find out how much Ira has after the 6 years in the first account and then how much he has after investing that total in the second account for 3 years, we can follow these steps:

Step 1: Calculate the account balance after 6 years of 5.6% simple interest.

The formula for simple interest is:
\[ I = P \times r \times t \] Where:
\(I\) = Interest earned
\(P\) = Principal amount (initial investment)
\(r\) = Annual interest rate (as a decimal)
\(t\) = Time in years

In this case:
\(P = 8000\)
\(r = 5.6% = 0.056\)
\(t = 6\)

Now we can calculate the interest earned:
\[ I = 8000 \times 0.056 \times 6 = 8000 \times 0.336 = 2688 \]

Now, we add the interest earned to the principal to get the total amount after 6 years:
\[ \text{Total Amount} = P + I = 8000 + 2688 = 10688 \]

Step 2: Calculate the new account balance after investing this amount in the account that earns 6% interest for 3 years.

Now we will use the same simple interest formula for the new investment. Here:
\(P = 10688\) (the total from the first account)
\(r = 6% = 0.06\)
\(t = 3\)

Calculating the interest earned in the new account:
\[ I = 10688 \times 0.06 \times 3 = 10688 \times 0.18 = 1923.84 \]

Now, add the interest earned to the principal to find the total account balance after 3 years:
\[ \text{Total Amount} = P + I = 10688 + 1923.84 = 12611.84 \]

Final Results:

• The amount Ira invests into the account that earns 6% simple interest is $10688.
• At the end of 3 years, the account balance is $12611.84.

Now we can fill in the responses:

Ira invests $10688 into the account that earns 6% simple interest. At the end of 3 years, the account balance is $12611.84.