Final answer:
To determine the amount after 8 years with a $270 initial deposit at an annual interest rate of 8 percent compounded annually, use the compound interest formula A = P(1 + r/n)^(nt) where P is the principal, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.
Step-by-step explanation:
The student is asking about how much money would be in a savings account after 8 years with an initial deposit of $270 and an annual interest rate of 8 percent, compounded annually. To find this, we can 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.
In this case, since the interest is compounded annually, n is 1. Therefore, the formula simplifies to:
A = 270(1 + 0.08)8
Now, calculate the amount:
A = 270(1 + 0.08)8 = 270(1.08)8
After calculating using the given values, you will find the total amount in the savings account after 8 years.