Final answer:
To determine the account balance after 10 years with compound interest, use the formula FV = P(1 + r/n)^(nt), which results in $488.67 with a $300 initial deposit, 5% annual interest, compounded annually, over 10 years.
Step-by-step explanation:
The subject question deals with compound interest, which is a fundamental concept in mathematics related to personal finance and investment. When money is deposited in a bank account that offers compound interest, the interest earned is added to the principal amount, and then the interest for the next period is calculated on the new total. This is different from simple interest, where interest is calculated on the original principal only.
To calculate the future value of an investment with compound interest, we use the formula:
FV = P(1 + r/n)^(nt)
Where:
- FV is the future value of the investment,
- P is the principal amount (the initial amount of money),
- r is the annual interest rate (in decimal form),
- n is the number of times that interest is compounded per year,
- t is the time the money is invested for in years.
In the case provided, you deposit $300 in an account with a 5% interest rate, compounded annually, and want to know how much you will have after 10 years.
Using the formula, we get:
FV = 300(1 + 0.05/1)^(1*10) = 300(1.05)^10
Calculating the power, we have:
FV = 300(1.62889) = 488.667
Therefore, after 10 years, you would have approximately $488.67 in the account, rounded to the nearest cent.