Explanation:
To calculate the interest that Nora will earn in three years on her $30 deposit with a 10% interest rate compounded annually, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
- A is the final amount (including interest)
- P is the principal amount (initial deposit)
- r is the interest rate (as a decimal)
- n is the number of compounding periods per year
- t is the time in years
In this case, Nora's principal amount (P) is $30, the interest rate (r) is 10% (0.10 as a decimal), the compounding period (n) is 1 (compounded annually), and the time (t) is 3 years.
Plugging in these values into the formula:
A = $30(1 + 0.10/1)^(1*3)
Simplifying the equation:
A = $30(1.10)^3
A ≈ $30(1.331)
A ≈ $39.93
To find the interest earned, we subtract the principal amount from the final amount:
Interest = A - P
Interest = $39.93 - $30
Interest ≈ $9.93
Therefore, Nora will earn approximately $9.93 in interest over three years.