Final answer:
Blanche's balance from Account 1 after 3.2 years, using the annual compounding interest formula, would be $9736.70, rounded to two decimal places.
Step-by-step explanation:
The student's question is about calculating the future value of an investment made in a Certificate of Deposit (CD) account that compounds annually.
To find out how much Blanche's balance would be from Account 1 over 3.2 years with an annual compound interest rate of 5.1%, we use the formula for compound interest:
A = P(1 + r/n)^(nt),
where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial sum of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
In Blanche's case, she is investing $8300 at a rate of 5.1% compounded annually for 3.2 years. Since the compounding is annual, n = 1. Therefore, the formula simplifies to:
A = 8300(1 + 0.051/1)^(1*3.2)
Calculating this, we get:
A = 8300(1 + 0.051)^(3.2)
A = 8300(1.051)^(3.2)
A = 8300(1.172)
So the final amount is:
A = 9736.70
Therefore, the balance in Account 1 after 3.2 years would be $9736.70, rounded to two decimal places.