You deposit \( \$ 3000 \) in an account earning \( 2 \% \) interest compounded monthly. How much will you have in the account in 10 years? Round value to the nearest cent. Question Help: Video

To find out how much you'll have in the account after 10 years with \( \$ 3000 \) deposited at \( 2\% \) interest compounded monthly, you can use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the amount in the account after time \( t \). - \( P \) is the principal amount (\$3000). - \( r \) is the annual interest rate (0.02). - \( n \) is the number of times interest is compounded per year (12). - \( t \) is the number of years the money is invested or borrowed (10). Plugging in the values: \[ A = 3000 \left(1 + \frac{0.02}{12}\right)^{12 \times 10} = 3000 \left(1 + \frac{0.02}{12}\right)^{120} \] Calculating this step-by-step, you would find that after 10 years, your account will have approximately \( \$ 3,677.64 \). It's like watching your money grow like a little plant: with each compounding month, it gets a little taller! Happy saving! For fun, you might also explore how interest rates impact your savings as you consider future investments. A small change can lead to a big difference over time! Check out savings calculators online to play with different deposit amounts and interest rates and see how your financial garden can flourish!