Prince's parents saved for his college education by investing Php 12,000 at the beginning of each year in an education plan that earns 6% interest compounded annually. What is the total amount of investment after 16 years?
Answer (1)
Answer:- Principal: Php 12,000 (the amount invested each year)- Interest Rate: 6% per year- Compounding Period: Annually (interest is calculated and added to the principal once a year)- Time: 16 years Formula for Compound Interest The formula for compound interest is: A = P(1 + r/n)^(nt) Where: - A = the future value of the investment/loan, including interest- P = the principal investment amount (the initial deposit or loan amount)- r = the annual interest rate (as a decimal)- n = the number of times that interest is compounded per year- t = the number of years the money is invested or borrowed for Calculations 1. Convert the interest rate to a decimal: 6% = 0.062. Identify the number of compounding periods per year: n = 1 (compounded annually)3. Calculate the future value of each year's investment:- Year 1: A = 12000(1 + 0.06/1)^(1*1) = Php 12,720- Year 2: A = 12000(1 + 0.06/1)^(1*2) = Php 13,483.20- ...and so on for each year.4. Add up the future values of each year's investment: This will give you the total amount after 16 years. Using a Spreadsheet or Financial Calculator Since we're dealing with multiple years, it's easier to use a spreadsheet or financial calculator to calculate the total amount. Here's how you can do it using a spreadsheet: 1. Set up your spreadsheet:- Column A: Year (1 to 16)- Column B: Investment Amount (Php 12,000 for each year)- Column C: Future Value (use the compound interest formula for each year)2. Calculate the future value for each year: Use the formula in Column C: =B2*(1+0.06)^A2 (assuming your investment amount is in cell B2 and year is in cell A2). Copy this formula down for all 16 years.3. Sum the future values: Use the SUM function in your spreadsheet to add up all the values in Column C. The total amount of investment after 16 years will be approximately Php 324,447.45. Important Note: This calculation assumes that the 6% interest rate remains constant throughout the 16 years. In real-world situations, interest rates can fluctuate.
