If Php 50,000 is invested for 10 years that earns an interest of 7.5% compounded semi-annually , how much would it be at the end of that time? (use the formula provided in problem)
Answer (2)
Step-by-step explanation:Calculating the Future Value Here's how to calculate the future value of the investment: Formula: Where: - is the future value- is the present value (initial investment)- is the annual interest rate- is the number of times interest is compounded per year- is the time in years Step 1: Identify the values: - - (7.5% expressed as a decimal)- (compounded semi-annually)- Step 2: Substitute the values into the formula: Step 3: Simplify the equation: Step 4: Calculate the future value: Therefore, the investment would be worth Php 103,051.50 at the end of 10 years.
Answer:To calculate the future value of an investment with compound interest, you can use the formula:\[A = P \left(1 + \frac{r}{n}\right)^{nt}\]Where:- \( A \) = the amount of money accumulated after n years, including interest.- \( P \) = the principal amount (the initial amount of money).- \( r \) = the annual interest rate (decimal).- \( n \) = the number of times that interest is compounded per year.- \( t \) = the number of years the money is invested or borrowed.For your problem:- \( P = 50,000 \)- \( r = 7.5\% = 0.075 \)- \( n = 2 \) (since the interest is compounded semi-annually)- \( t = 10 \)Now, plug these values into the formula:\[A = 50000 \left(1 + \frac{0.075}{2}\right)^{2 \times 10}\]Calculating step by step:1. Calculate \( \frac{r}{n} \): \[ \frac{0.075}{2} = 0.0375 \]2. Calculate \( nt \): \[ 2 \times 10 = 20 \]3. Substitute into the formula: \[ A = 50000 \left(1 + 0.0375\right)^{20} \] \[ A = 50000 \left(1.0375\right)^{20} \]4. Calculate \( (1.0375)^{20} \): \[ (1.0375)^{20} \approx 2.030857 \]5. Now, multiply by the principal: \[ A \approx 50000 \times 2.030857 \approx 101542.85 \]Thus, the amount at the end of 10 years would be approximately **Php 101,542.85**.
