Question

Alma deposits $725 in an account that earns 3% interest each year. After the first year, Alma has $746.75 in the account. After the second year, Alma has $768.50 in the account, and after the third year, Alma has $790.25 in the account.

Answer 1

Alma deposited $725 in an account that earns 3% interest annually. The account is compounded annually.

Explanation:

Alma's initial deposit of $725 grows to $746.75 after the first year, $768.50 after the second year, and $790.25 after the third year, with a consistent 3% interest rate annually. To calculate this, we can use the formula for compound interest:
`\[A = P * (1 + r)^n\]`, where A is the final amount, P is the principal amount, ris the annual interest rate, and n is the number of years. By plugging in the given values for each year, the pattern suggests that the interest is compounded annually.

Rearranging the formula to find the final amount after each year using the given values confirms the consistency of the 3% annual interest rate. The sequence of amounts at the end of each year aligns with the expected growth from compounding interest annually over the three-year period.

Alma's account demonstrates the compounding effect of interest, where the interest earned in each period contributes to the principal amount for subsequent calculations. This consistent growth aligns with the expectations of compound interest, confirming the 3% interest rate is compounded annually over the three-year period.