On July 1, 1996, Anna invested $2000 in an account that earned 6%/a compounded monthly. On July 1, 2001, she moved the total amount to a new account that paid 8%/a compounded quarterly. Determine the balance in her new account on January 1, 2008.
To determine the balance in Anna's new account on January 1, 2008, we need to break down the problem into two separate parts: calculating the balance on July 1, 2001, and then calculating the balance from July 1, 2001, to January 1, 2008.
1. Calculating the balance on July 1, 2001:
- Anna invested $2000 on July 1, 1996, at an annual interest rate of 6% compounded monthly.
- To calculate the balance on July 1, 2001, we need to determine the future value of this investment using the compound interest formula:
Future Value = Principal * (1 + (annual interest rate / number of compounding periods))^(number of compounding periods * number of years)
Here, Principal = $2000, Annual interest rate = 6% = 0.06, Number of compounding periods per year = 12, Number of years = 5.
Plugging in the values into the formula:
Future Value = $2000 * (1 + (0.06 / 12))^(12 * 5)
Evaluating this expression gives us the balance on July 1, 2001.
2. Calculating the balance from July 1, 2001, to January 1, 2008:
- On July 1, 2001, Anna moved the total amount to a new account that paid 8% interest compounded quarterly.
- To calculate the balance on January 1, 2008, we will use the same compound interest formula, but with the following values:
Principal = The balance on July 1, 2001 (obtained in step 1)
Annual interest rate = 8% = 0.08
Number of compounding periods per year = 4
Number of years = 6.5 (from July 1, 2001, to January 1, 2008)
Plugging in these values into the formula, we can find the final balance on January 1, 2008.
By following these steps, you can calculate the balance in Anna's new account on January 1, 2008.