1. Let's talk about saving money and how it grows over time when you put it in a bank or somewhere that gives you extra money called interest. 2. Imagine you put some money in a piggy bank every year. The money you put in earlier gets bigger because of interest. The formula to find out how much your money will be later is called the Future Value (FV) formula: $$FV = PV \times (1 + r)^t$$ where: - $PV$ is the money you put in (the principal), - $r$ is the interest rate (like 7% or 8%, but written as 0.07 or 0.08), - $t$ is how many years you wait. 3. When you put money in different years, you find the future value of each amount separately, then add them all up. 4. For example, if you put 100 in year 1, 200 in year 2, and 300 in year 3, and the interest rate is 7%, to find how much you have at year 3: - The 100 you put in year 1 grows for 2 years: $$100 \times (1 + 0.07)^2$$ - The 200 you put in year 2 grows for 1 year: $$200 \times (1 + 0.07)^1$$ - The 300 you put in year 3 doesn't grow because you just put it in. 5. Add them all: $$FV_3 = 100 \times 1.07^2 + 200 \times 1.07 + 300 = 114.49 + 214 + 300 = 628.49$$ 6. The interest you earned is the total money minus what you put in: $$Interest = 628.49 - (100 + 200 + 300) = 28.49$$ 7. If you wait until year 5 without adding more money, the money you had at year 3 grows for 2 more years: $$FV_5 = 628.49 \times (1 + 0.07)^2 = 628.49 \times 1.07^2 = 719.56$$ 8. So, your money grows bigger and bigger the longer you wait! 9. This is how banks help your money grow with interest over time. 10. Remember, each amount you put in grows for the number of years left until you check your money. That's the simple way to understand how money grows with interest over time!