1. **Problem statement:** A sum of 6000 is to be paid back in two equal annual installments at the end of each year. The interest rate is 2% compounded annually. We need to find the amount of each installment. 2. **Understanding the problem:** Let each installment be $x$. The present value (PV) of the two installments must equal 6000. 3. **Formula for present value of installments:** The first installment is paid after 1 year, so its present value is $\frac{x}{(1+0.02)^1} = \frac{x}{1.02}$. The second installment is paid after 2 years, so its present value is $\frac{x}{(1+0.02)^2} = \frac{x}{1.02^2} = \frac{x}{1.0404}$. 4. **Set up the equation:** $$6000 = \frac{x}{1.02} + \frac{x}{1.0404}$$ 5. **Combine terms:** $$6000 = x \left(\frac{1}{1.02} + \frac{1}{1.0404}\right) = x \left(0.98039 + 0.96117\right) = x \times 1.94156$$ 6. **Solve for $x$:** $$x = \frac{6000}{1.94156} \approx 3089.16$$ 7. **Answer:** Each installment is approximately **3089.16**.