1. **State the problem:** Solve for $r$ in the equation $$930=35\times\left(\frac{1-(1+r)^{-54}}{r}\right)+\frac{1000}{(1+r)^{54}}.$$\n\n2. **Understand the formula:** This equation resembles the present value of an annuity plus a lump sum discounted at rate $r$. The term $$35\times\left(\frac{1-(1+r)^{-54}}{r}\right)$$ is the present value of an annuity paying 35 for 54 periods, and $$\frac{1000}{(1+r)^{54}}$$ is the present value of 1000 received at period 54.\n\n3. **Rewrite the equation for clarity:**\n$$930 = 35 \cdot \frac{1-(1+r)^{-54}}{r} + \frac{1000}{(1+r)^{54}}.$$\n\n4. **Isolate terms and simplify:** This is a nonlinear equation in $r$ and cannot be solved algebraically in closed form easily. We use numerical methods (e.g., Newton-Raphson) to approximate $r$.\n\n5. **Set function $f(r)$ to zero:**\n$$f(r) = 35 \cdot \frac{1-(1+r)^{-54}}{r} + \frac{1000}{(1+r)^{54}} - 930 = 0.$$\n\n6. **Numerical approximation:** Using iterative methods or financial calculator, approximate $r \approx 0.037$ (or 3.7%).\n\n**Final answer:**\n$$r \approx 0.037.$$