Loan Decision 226Bb6

1. **Problem Statement:** You have P300,000 in a savings account earning 0.3% monthly interest. You need P900,000 to buy a car. You have two options: - Let your savings earn interest for 3 years and then get Loan A. - Use your savings to get Loan B. 2. **Given Data:** - Initial savings $P = 300,000$ - Monthly interest rate on savings $r_s = 0.3\% = 0.003$ - Time saving $n_s = 3$ years $= 36$ months - Loan A: $900,000$ for $36$ months at $0.8\%$ monthly interest, monthly payment $A_A = 22,089.10$ - Loan B: $600,000$ for $24$ months at $0.6\%$ monthly interest, monthly payment $A_B = 23,046$ 3. **Step 1: Calculate future value of savings after 3 years** Formula for future value of periodic investments (or savings): $$FV = P(1 + r_s)^n_s$$ Calculate: $$FV = 300,000 \times (1 + 0.003)^{36}$$ Calculate the power: $$ (1.003)^{36} \approx 1.1136$$ So, $$FV = 300,000 \times 1.1136 = 334,080$$ 4. **Step 2: Compare future savings with needed amount** You need P900,000 but after 3 years your savings will be approximately P334,080, which is less than P900,000. 5. **Step 3: Analyze Loan A** Loan A amount: P900,000 Monthly payment: P22,089.10 Number of payments: 36 Interest rate: 0.8% monthly 6. **Step 4: Analyze Loan B** Loan B amount: P600,000 Monthly payment: P23,046 Number of payments: 24 Interest rate: 0.6% monthly 7. **Step 5: Decision** - If you wait 3 years, your savings grow to P334,080, which is not enough to buy the car outright. - Loan A covers the full amount but has a longer term and lower monthly payment. - Loan B requires a higher monthly payment but is for a smaller loan and shorter term. 8. **Conclusion:** You should consider your ability to pay monthly installments. If you can afford P22,089.10 monthly for 36 months, Loan A is suitable. If you want to pay off faster and can afford P23,046 monthly for 24 months, Loan B is better. Since your savings alone are insufficient, taking a loan is necessary. **Final answer:** You should either wait 3 years to grow your savings and then take Loan A for the remaining amount or use your savings now and take Loan B. The choice depends on your monthly payment capacity.