1. **Problem Statement:** Calculate and compare the interest for each loan package given the loan amount of 500000 and loan term of 10 years. 2. **Formulas and Rules:** - For simple interest: $$I = P \times r \times t$$ where $P$ is principal, $r$ is annual interest rate (decimal), and $t$ is time in years. - For compound interest: $$A = P \times (1 + r)^t$$ and interest $$I = A - P$$. - For one-time payment with total interest rate: Interest is calculated as $$I = P \times R$$ where $R$ is total interest rate over the term. 3. **Calculations:** **Package 1 (Simple Interest 5% per annum):** $$I_1 = 500000 \times 0.05 \times 10 = 250000$$ **Package 2 (One-time Interest 45% total):** $$I_2 = 500000 \times 0.45 = 225000$$ **Package 3 (Compound Interest 4.2% annually):** $$A_3 = 500000 \times (1 + 0.042)^{10} = 500000 \times (1.042)^{10}$$ Calculate $(1.042)^{10}$: $$1.042^{10} \approx 1.502$$ So, $$A_3 \approx 500000 \times 1.502 = 751000$$ Interest: $$I_3 = 751000 - 500000 = 251000$$ **Installment Package (5% compound annually, monthly payments 20000):** This is more complex; the loan is paid monthly over 10 years (120 months) with interest compounded annually on remaining principal after each payment. Approximate total payment: $$20,000 \times 120 = 2,400,000$$ Since this is much higher than principal, interest is substantial but exact interest requires amortization calculation. 4. **Comparison:** - Package 1 interest: 250000 - Package 2 interest: 225000 - Package 3 interest: 251000 - Installment package total payments: 2,400,000 (much higher, includes principal and interest) 5. **Choice:** Package 2 has the lowest total interest (225000) and is a one-time payment, which might be preferable if you can invest the money elsewhere. 6. **Custom Installment Package Suggestion:** Choose a monthly payment that balances affordability and total interest paid. For example, increasing monthly payments reduces interest but increases monthly burden. A detailed amortization schedule would help optimize this. Final answer: Package 2 has the lowest interest cost of 225000.