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Help: Video 1 Video 2 Message instructor 2 0//3 pts sit $500 each month into an account earning 5% interest compounded uch will you have in the account in 20 years? ich total money will you put into the account?

Help:\newlineVideo 11\newlineVideo 22\newlineMessage instructor\newline22\newline0/3 0 / 3 pts\newlinesit \$\(500\) each month into an account earning \(5\)\% interest compounded\(\newline\)uch will you have in the account in \(20\) years?\(\newline\)ich total money will you put into the account?

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Q. Help:\newlineVideo 11\newlineVideo 22\newlineMessage instructor\newline22\newline0/3 0 / 3 pts\newlinesit \$\(500\) each month into an account earning \(5\)\% interest compounded\(\newline\)uch will you have in the account in \(20\) years?\(\newline\)ich total money will you put into the account?
  1. Identify variables: Identify the variables for the compound interest formula for monthly contributions.\newlineWe have:\newlineMonthly deposit (PMT) = $500\$500\newlineAnnual interest rate (r) = 5%5\% or 0.050.05\newlineNumber of years (t) = 2020\newlineCompounding frequency per year (n) = 1212 (since it's compounded monthly)\newlineTotal number of deposits (nt) = n×t=12×20=240n \times t = 12 \times 20 = 240
  2. Convert interest rate: Convert the annual interest rate to a monthly interest rate.\newlineMonthly interest rate ii = Annual interest rate / Compounding frequency per year\newlinei=rn=0.0512≈0.0041667i = \frac{r}{n} = \frac{0.05}{12} \approx 0.0041667
  3. Calculate future value: Use the future value of a series formula for compound interest to calculate the total amount in the account after 2020 years.\newlineThe formula is:\newlineFV=PMT×((1+i)nt−1)/iFV = PMT \times \left(\left(1 + i\right)^{nt} - 1\right) / i
  4. Plug values and calculate: Plug the values into the formula and calculate the future value.\newlineFV=500×((1+0.0041667)240−1)/0.0041667FV = 500 \times \left(\left(1 + 0.0041667\right)^{240} - 1\right) / 0.0041667\newlineFV≈500×((1.0041667)240−1)/0.0041667FV \approx 500 \times \left(\left(1.0041667\right)^{240} - 1\right) / 0.0041667
  5. Perform calculations: Perform the calculations.\newlineFV≈500×(((1.0041667)240−1)/0.0041667)FV \approx 500 \times (((1.0041667)^{240} - 1) / 0.0041667)\newlineFV≈500×((2.718987−1)/0.0041667)FV \approx 500 \times ((2.718987 - 1) / 0.0041667)\newlineFV≈500×(1.718987/0.0041667)FV \approx 500 \times (1.718987 / 0.0041667)\newlineFV≈500×412.477FV \approx 500 \times 412.477\newlineFV≈206238.5FV \approx 206238.5
  6. Calculate total deposits: Calculate the total money deposited into the account over 2020 years.\newlineTotal deposits == Monthly deposit ×\times Total number of deposits\newlineTotal deposits =500×240= 500 \times 240\newlineTotal deposits =120000= 120000

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