Loan Interest Calculation 928823

1. **State the problem:** A computer is bought by paying an initial amount of $10000$ and the rest is paid in $10$ equal monthly installments of $8800$ each. The outright payment price is $900000$. We need to find: - Balance to be paid as loan - Total interest to be paid - Number of months for which interest is paid - Interest per month - Annual interest rate 2. **Calculate the balance to be paid as loan:** The total price is $900000$. Initial payment = $10000$ Loan amount = Total price $-$ Initial payment $$\text{Loan} = 900000 - 10000 = 890000$$ 3. **Calculate the total amount paid in installments:** Number of installments = $10$ Each installment = $8800$ Total installments paid = $10 \times 8800 = 88000$ 4. **Calculate the total interest paid:** Total amount paid = Initial payment + Total installments $$\text{Total paid} = 10000 + 88000 = 98000$$ Interest paid = Total paid $-$ Loan amount $$\text{Interest} = 98000 - 890000 = \cancel{98000} - 890000 = -792000$$ This negative value indicates a misunderstanding in the problem statement or data. Usually, the loan amount should be the remaining price after initial payment, and installments should sum to more than loan amount to include interest. Assuming the problem meant the computer price is $90000$ (not $900000$), let's recalculate: Loan = $90000 - 10000 = 80000$ Total installments = $10 \times 8800 = 88000$ Total paid = $10000 + 88000 = 98000$ Interest = $98000 - 80000 = 18000$ 5. **Months for which interest is paid:** Given $10$ installments, interest is paid over $10$ months. 6. **Interest per month:** $$\text{Interest per month} = \frac{18000}{10} = 1800$$ 7. **Calculate the rate of annual interest:** Principal = $80000$ Interest = $18000$ Time = $10$ months = $\frac{10}{12}$ years Using simple interest formula: $$I = P \times R \times T$$ Solve for $R$: $$R = \frac{I}{P \times T} = \frac{18000}{80000 \times \frac{10}{12}} = \frac{18000}{80000 \times 0.8333} = \frac{18000}{66666.67} = 0.27 = 27\%$$ **Final answers:** 1. Balance to be paid as loan = $80000$ 2. Total interest to be paid = $18000$ 3. Months interest is paid = $10$ 4. Interest per month = $1800$ 5. Annual interest rate = $27\%$