Ask AI: If you save $300 a month for 50 years (age 20 to 70) at 10% interest, how much money will you have?

To determine how much money you will have after saving $300 a month for 50 years at an annual interest rate of 10%, you can use the future value of an annuity formula. The formula to calculate the future value of an annuity (FV) is: \[ FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \] where: - \( P \) is the monthly contribution ($300) - \( r \) is the monthly interest rate (annual rate divided by 12) - \( n \) is the total number of contributions (months) First, let's break down the components: 1. Annual interest rate (\( I \)) = 10% = 0.10 2. Monthly interest rate (\( r \)) = 0.10 / 12 = 0.0083333 3. Total number of months (\( n \)) = 50 years × 12 months/year = 600 months Now plug these values into the formula: \[ FV = 300 \times \left( \frac{(1 + 0.0083333)^{600} - 1}{0.0083333} \right) \] Calculate: 1. \( (1 + 0.0083333)^{600} = (1.0083333)^{600} \approx 117.40 \) (using a calculator or a computation tool) 2. Subtract 1: \( 117.40 - 1 = 116.40 \) 3. Divide by the monthly interest rate: \( 116.40 / 0.0083333 \approx 13964.04 \) 4. Multiply by the monthly contribution: \( 300 \times 13964.04 = 4,189,212 \) Therefore, if you save $300 a month for 50 years at an annual interest rate of 10%, you will have approximately $4,189,212.