1. **State the problem:** A loan of 3624 is borrowed today and repaid in three equal installments due at 1.5 years, 3.5 years, and 5.5 years. The interest rate is 7.7% compounded monthly. We need to find the size of each equal installment. 2. **Identify the interest rate per month:** The annual nominal interest rate is 7.7%, so the monthly interest rate is $$i = \frac{7.7}{100 \times 12} = 0.0064167$$ (approximately). 3. **Calculate the present value of each installment:** Let the installment amount be $X$. The present value (PV) of each installment discounted to today is: - For the installment at 1.5 years (18 months): $$\frac{X}{(1 + i)^{18}}$$ - For the installment at 3.5 years (42 months): $$\frac{X}{(1 + i)^{42}}$$ - For the installment at 5.5 years (66 months): $$\frac{X}{(1 + i)^{66}}$$ 4. **Set up the equation for the loan amount:** The sum of the present values of the three installments equals the loan amount: $$3624 = X \left(\frac{1}{(1 + 0.0064167)^{18}} + \frac{1}{(1 + 0.0064167)^{42}} + \frac{1}{(1 + 0.0064167)^{66}}\right)$$ 5. **Calculate the discount factors:** - $$ (1 + 0.0064167)^{18} \approx 1.1275 $$ - $$ (1 + 0.0064167)^{42} \approx 1.3025 $$ - $$ (1 + 0.0064167)^{66} \approx 1.5055 $$ 6. **Calculate the sum of the present value factors:** $$ S = \frac{1}{1.1275} + \frac{1}{1.3025} + \frac{1}{1.5055} \approx 0.8867 + 0.7675 + 0.6641 = 2.3183 $$ 7. **Solve for $X$:** $$ X = \frac{3624}{2.3183} \approx 1563.3 $$ **Final answer:** Each equal installment is approximately $1563.30.