Final answer:
To calculate the difference between the interest earned on Miguel's $1,000 deposit and the interest earned on Valeria's $1,000 deposit, we need to use the formulas for simple interest and compound interest. For Miguel's deposit, the simple interest is calculated by multiplying the principal amount ($1,000) by the interest rate (4%) and the number of years (4): $1,000 * 0.04 * 4 = $160. For Valeria's deposit, the compound interest is calculated using the formula: A = P(1 + r/n)^(nt). The difference between the interest earned on Miguel's and Valeria's deposit is $1,048.16 - $1,000 = $48.16.
Step-by-step explanation:
To calculate the difference between the interest earned on Miguel's $1,000 deposit and the interest earned on Valeria's $1,000 deposit, we need to use the formulas for simple interest and compound interest. For Miguel's deposit, the simple interest is calculated by multiplying the principal amount ($1,000) by the interest rate (4%) and the number of years (4): $1,000 * 0.04 * 4 = $160. For Valeria's deposit, the compound interest is calculated using the formula:
A = P(1 + r/n)^(nt)
Where A is the amount, P is the principal amount, r is the interest rate, n is the number of times compounded per year, and t is the number of years. Plugging in the values, we get:
A = $1,000(1 + 0.04/1)^(1*4) = $1,048.16
The difference between the interest earned on Miguel's and Valeria's deposit is $1,048.16 - $1,000 = $48.16.