Final answer:
The simple interest is $300, while the compound interest earned when investing the same sum for 2 years at 5% is $102.5.
Step-by-step explanation:
The simple interest earned when you invest $1,000 for 3 years at 10% can be calculated using the formula: Principal × Rate × Time = Interest.
In this case, $1,000 × 0.10 × 3
= $300.
The compound interest earned when you invest the same sum for 2 years at 5% can be calculated using the formula: A = P(1 + r/n)^(nt) - P, (where A is the total amount, P is the principal, r is the interest rate, n is the number of compounding periods per year, and t is the number of years).
Plugging in the values, we get:
A = $1,000(1 + 0.05/1)^(1 × 2) - $1,000
= $1,000(1.05)^2 - $1,000
= $1,102.5 - $1,000
= $102.5.