1. **Problem Statement:** Farah bought a television priced at 6200 with 10% down payment and equal monthly payments for 15 months. Interest is 7% on reducing balance. Calculate: (a) Monthly payment (b) Instalment price (c) Outstanding balance after 8th payment using rule of 78. 2. **Formulas and Rules:** - Down payment = 10% of 6200 = 0.10 \times 6200 = 620 - Principal financed = 6200 - 620 = 5580 - Interest rate per year = 7% = 0.07 - Number of months = 15 - Reducing balance interest means interest is charged on remaining principal after each payment. - Rule of 78 is a method to allocate interest over loan period: sum of digits = \frac{n(n+1)}{2} = \frac{15 \times 16}{2} = 120 --- ### (a) Monthly Payment 3. Calculate total interest over 15 months on reducing balance: Since interest is on reducing balance, monthly interest rate = \frac{0.07}{12} = 0.0058333 4. Use amortization formula for monthly payment $M$: $$M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$$ where $P=5580$, $r=0.0058333$, $n=15$ 5. Calculate $(1+r)^n$: $$ (1+0.0058333)^{15} = 1.0931 $$ 6. Substitute values: $$M = 5580 \times \frac{0.0058333 \times 1.0931}{1.0931 - 1} = 5580 \times \frac{0.006375}{0.0931} = 5580 \times 0.06847 = 381.9$$ So monthly payment $M \approx 381.90$ --- ### (b) Instalment Price 7. Instalment price = down payment + total of monthly payments Total monthly payments = $381.90 \times 15 = 5728.5$ Instalment price = $620 + 5728.5 = 6348.5$ --- ### (c) Outstanding Balance after 8th Payment using Rule of 78 8. Total interest = Instalment price - cash price = 6348.5 - 6200 = 148.5 9. Sum of digits = 120 10. Interest paid in first 8 months = $\frac{15+14+...+(15-8+1)}{120} \times 148.5$ Sum of first 8 months digits = $15+14+13+12+11+10+9+8 = 92$ Interest paid in 8 months = $\frac{92}{120} \times 148.5 = 113.85$ 11. Principal repaid in 8 months = total paid - interest paid = $381.9 \times 8 - 113.85 = 3055.2 - 113.85 = 2941.35$ 12. Outstanding balance = principal financed - principal repaid = $5580 - 2941.35 = 2638.65$ --- **Final answers:** (a) Monthly payment = **381.90** (b) Instalment price = **6348.50** (c) Outstanding balance after 8th payment = **2638.65**