1. **State the problem:** We have a loan of 23150 at an annual interest rate of 6% compounded semi-annually. Payments are made every 6 months, and the loan is settled in 5 years. We need to find: a) The size of each periodic payment. b) The total interest paid. 2. **Identify variables:** - Principal, $P = 23150$ - Annual interest rate, $r = 0.06$ - Compounding periods per year, $m = 2$ (semi-annually) - Number of years, $t = 5$ - Total number of payments, $n = m \times t = 2 \times 5 = 10$ - Periodic interest rate, $i = \frac{r}{m} = \frac{0.06}{2} = 0.03$ 3. **Formula for periodic payment $A$ of an amortized loan:** $$ A = P \times \frac{i(1+i)^n}{(1+i)^n - 1} $$ 4. **Calculate $(1+i)^n$:** $$ (1+0.03)^{10} = 1.03^{10} \approx 1.34392 $$ 5. **Calculate numerator:** $$ 0.03 \times 1.34392 = 0.0403176 $$ 6. **Calculate denominator:** $$ 1.34392 - 1 = 0.34392 $$ 7. **Calculate fraction:** $$ \frac{0.0403176}{0.34392} \approx 0.11728 $$ 8. **Calculate periodic payment $A$:** $$ A = 23150 \times 0.11728 \approx 2713.89 $$ 9. **Answer for part (a):** The size of the periodic payment is approximately $2713.89$. 10. **Calculate total amount paid:** $$ \text{Total paid} = A \times n = 2713.89 \times 10 = 27138.90 $$ 11. **Calculate total interest paid:** $$ \text{Interest} = \text{Total paid} - P = 27138.90 - 23150 = 3988.90 $$ 12. **Answer for part (b):** The total interest paid is approximately $3988.90$. **Final answers:** - a) $2713.89$ - b) $3988.90$