A man bought a lot worth P1000000 if paid in cash.
On an installment basis, he paid a down payment of
P200,000.00, P300,000.00 at the end of one year,
P400,000.00 at the end of three years, and a final
payment at the end of five years. What was the final
payment if the interest was 20%?
Answer (1)
Here's how to solve this problem step-by-step: 1. Calculate the remaining balance after the down payment: - Total cost: ₱1,000,000 - Down payment: ₱200,000 - Remaining balance: ₱1,000,000 - ₱200,000 = ₱800,000 2. Calculate the future value of each installment payment: We need to find the future value of each installment at the end of the five-year period to determine how much each payment is worth at that time. We'll use the future value formula: FV = PV (1 + i)^n Where: - FV = Future Value - PV = Present Value (the installment payment) - i = interest rate (per year) - n = number of years - First Installment (₱300,000 at the end of year 1): - FV = 300,000 * (1 + 0.20)^(5-1) = 300,000 * (1.20)^4 = ₱691,200 - Second Installment (₱400,000 at the end of year 3): - FV = 400,000 * (1 + 0.20)^(5-3) = 400,000 * (1.20)^2 = ₱576,000 3. Calculate the total future value of the installments: - Total FV of installments: ₱691,200 + ₱576,000 = ₱1,267,200 4. Calculate the future value of the remaining balance: The remaining balance of ₱800,000 also accrues interest over the five years. - FV = 800,000 * (1 + 0.20)^5 = 800,000 * (1.20)^5 = ₱2,488,320 5. Calculate the final payment: The final payment is the difference between the future value of the remaining balance and the total future value of the installments already made. - Final Payment = ₱2,488,320 - ₱1,267,200 = ₱1,221,120 Answer: The final payment at the end of five years was ₱1,221,120.please give me a heart in exchange thank you
