What I Can Do Money Matters Read and analyze the given situation below. Answer the questions that follow. DE You are a regular employee in a finance company that offers a loan payable through salary deduction. One of its privileges is availing a loan that offers a 5% interest compounded annually for 1 to 5 years. You are thinking to apply for a loan but you wanted to analyze if you can shoulder the monthly payment. Make a loan schedule and fill up an application form that will help you decide the amount of loan that you will make Loan Schedule EDUCATION Monthly Payment Loan Amount Maturity Value t-5 P10,000 P20,000 P30,000 P40,000 P50,000 P100,000 P150,000 P200,000 P250,000 21need help with complete solution
Answer (1)
Answer:To analyze if you can afford the monthly payment and decide on the loan amount, let's break down the process step by step. Since the loan offers 5% interest compounded annually, we need to calculate the maturity value of each loan amount and the corresponding monthly payments.Step 1: Understanding the Formula for Compound InterestThe formula for compound interest to calculate the maturity value (A) is:A = P(1 + r/n)^{nt}Where:A is the maturity value (total amount to be repaid).P is the principal (loan amount).r is the annual interest rate (5% or 0.05).n is the number of times interest is compounded per year (since it's compounded annually, n = 1).t is the loan term in years.Step 2: Example Calculations for Loan Amounts Over 5 YearsLet's calculate the maturity value for each loan amount at the end of 5 years.1. Loan Amount = ₱10,000A = 10,000(1 + 0.05/1)^{1 \times 5} = 10,000(1.05)^5 ≈ 10,000(1.276281) = ₱12,762.812. Loan Amount = ₱20,000A = 20,000(1.05)^5 ≈ 20,000 \times 1.276281 = ₱25,525.633. Loan Amount = ₱30,000A = 30,000(1.05)^5 ≈ 30,000 \times 1.276281 = ₱38,288.444. Loan Amount = ₱40,000A = 40,000(1.05)^5 ≈ 40,000 \times 1.276281 = ₱51,051.265. Loan Amount = ₱50,000A = 50,000(1.05)^5 ≈ 50,000 \times 1.276281 = ₱63,814.076. Loan Amount = ₱100,000A = 100,000(1.05)^5 ≈ 100,000 \times 1.276281 = ₱127,628.157. Loan Amount = ₱150,000A = 150,000(1.05)^5 ≈ 150,000 \times 1.276281 = ₱191,442.228. Loan Amount = ₱200,000A = 200,000(1.05)^5 ≈ 200,000 \times 1.276281 = ₱255,256.309. Loan Amount = ₱250,000A = 250,000(1.05)^5 ≈ 250,000 \times 1.276281 = ₱319,070.37Step 3: Monthly Payment CalculationSince these loans are payable in 5 years (60 months), we can calculate the monthly payments by dividing the maturity value by 60.1. For ₱10,000 loan:\text{Monthly Payment} = \frac{12,762.81}{60} ≈ ₱212.712. For ₱20,000 loan:\text{Monthly Payment} = \frac{25,525.63}{60} ≈ ₱425.433. For ₱30,000 loan:\text{Monthly Payment} = \frac{38,288.44}{60} ≈ ₱638.144. For ₱40,000 loan:\text{Monthly Payment} = \frac{51,051.26}{60} ≈ ₱850.855. For ₱50,000 loan:\text{Monthly Payment} = \frac{63,814.07}{60} ≈ ₱1,063.576. For ₱100,000 loan:\text{Monthly Payment} = \frac{127,628.15}{60} ≈ ₱2,127.147. For ₱150,000 loan:\text{Monthly Payment} = \frac{191,442.22}{60} ≈ ₱3,190.708. For ₱200,000 loan:\text{Monthly Payment} = \frac{255,256.30}{60} ≈ ₱4,254.279. For ₱250,000 loan:\text{Monthly Payment} = \frac{319,070.37}{60} ≈ ₱5,317.84Step 4: Loan Schedule Summary
