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Tristan opened a savings account and deposited $200.00 as principal. The account earns 8% interest, compounded quarterly. How much interest will he earn after 8 years?

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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.

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