1. **State the problem:** Mr Adams invested 5000 and received 5810 after 3 years with simple interest. We need to find how long it will take for the investment to double (i.e., reach 10000) at the same interest rate. 2. **Formula for simple interest:** $$A = P(1 + rt)$$ where $A$ is the amount after time $t$, $P$ is the principal, $r$ is the annual interest rate, and $t$ is the time in years. 3. **Find the interest rate $r$ using the given data:** Given $P=5000$, $A=5810$, and $t=3$, substitute into the formula: $$5810 = 5000(1 + 3r)$$ 4. **Solve for $r$:** $$\frac{5810}{5000} = 1 + 3r$$ $$1.162 = 1 + 3r$$ $$3r = 1.162 - 1 = 0.162$$ $$r = \frac{0.162}{3} = 0.054$$ 5. **Find time $t$ to double the investment:** We want $A = 2P = 10000$, so: $$10000 = 5000(1 + 0.054t)$$ 6. **Solve for $t$:** $$\frac{10000}{5000} = 1 + 0.054t$$ $$2 = 1 + 0.054t$$ $$0.054t = 2 - 1 = 1$$ $$t = \frac{1}{0.054} \approx 18.52$$ **Final answer:** It will take approximately 18.52 years for Mr Adams' investment to double at the same interest rate.