1. **Problem Statement:** Calculate the simple interest rate and express the amount as a function of time. 2. **Formula for Simple Interest:** $$ A = P + Prt = P(1 + rt) $$ where $A$ is the amount after time $t$, $P$ is the principal, $r$ is the annual interest rate, and $t$ is time in years. 3. **Given Data:** - Principal $P = 400$ - Amount after 1 year $A_1 = 420$ - Amount after 2 years $A_2 = 440$ - Amount after 3 years $A_3 = 460$ 4. **Calculate Interest Rate $r$:** From the first year, $$ 420 = 400(1 + r \times 1) $$ $$ 1 + r = \frac{420}{400} = 1.05 $$ $$ r = 0.05 $$ or 5% per year. 5. **Write the amount function:** $$ A(t) = 400(1 + 0.05t) = 400 + 20t $$ 6. **Interpretation:** The loan grows by 20 each year, consistent with the table values. **Final answer:** The simple interest rate is 5% per year, and the amount after $t$ years is $$ A(t) = 400 + 20t $$