Final answer:
After nine years, by depositing $310 today into an account with a 9% annual interest rate, compounded annually, your savings account would have $601.02.
Step-by-step explanation:
To find out how much would be in your savings account in nine years after depositing $310 today if the bank pays 9 percent per year, you 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 amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
Given that the interest is compounded annually (n=1) and there are no intermediate deposits or withdrawals, your calculation would be:
A = $310 (1 + 0.09/1)^(1*9)
Calculating the parentheses first:
A = $310 (1.09)^9
Now, calculating the exponential part:
A = $310 * 1.9388467
Multiplying this out gives you:
A = $601.02
So, after nine years, your savings account would have $601.02 if you deposited $310 today into an account with a 9% annual interest rate, compounded annually.