Final answer:
To calculate the interest earned after 8 years on Tristan's $200.00 deposit with an 8% annual interest rate, compounded quarterly, use the compound interest formula. After calculating the total accumulated amount, subtract the principal to find the interest earned.
Step-by-step explanation:
Calculating Compound Interest Earned on a Savings Account
Tristan deposited $200.00 into a savings account that earns 8% interest, compounded quarterly. To calculate the interest earned after 8 years, we can use the compound interest formula:
A = P(1 + \frac{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 (in decimal form).
n is the number of times that interest is compounded per year.
t is the time in years.
Given that the principal P is $200, the annual interest rate r is 0.08 (since 8% as a decimal is 0.08), the number of times interest is compounded quarterly n is 4, and the time t is 8 years, we can plug these values into the formula to calculate the total amount A.
A = 200(1 + \frac{0.08}{4})^{4\times8}
Calculating this gives us the total amount that Tristan's account will have after 8 years. To find the interest earned, we subtract the initial deposit (the principal) from this total amount.
The exact amount of interest earned can be calculated using a calculator or other computing tools since the calculation can become complex due to exponents and decimal places involved.