You deposit \( \$ 3000 \) in an account earning \( 7 \% \) interest compounded monthly. How much will you have in the account in 5 years? \( \$ \) Enter an integer or decimal number more.] Calculator

To calculate the amount in your account after 5 years with \( \$ 3000 \) deposited at \( 7\% \) interest compounded monthly, you can use the formula: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial deposit). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of times that interest is compounded per year. - \( t \) is the number of years the money is invested for. Plugging in your values: - \( P = 3000 \) - \( r = 0.07 \) (which is \( 7\% \)) - \( n = 12 \) (monthly compounding) - \( t = 5 \) So, the calculation becomes: \[ A = 3000 \left(1 + \frac{0.07}{12}\right)^{12 \times 5} \] Let's break it down: 1. Calculate \( \frac{0.07}{12} \approx 0.00583333 \). 2. Now calculate \( 1 + 0.00583333 \approx 1.00583333 \). 3. The exponent \( 12 \times 5 = 60 \). 4. Now calculate \( A = 3000 \times (1.00583333)^{60} \approx 3000 \times 1.48985 \approx 4469.56 \). So, after 5 years, you will have approximately \( \$ 4469.56 \) in the account.