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Skills Quiz - Finance\newlineScore: 00/4040\newline00/1010 answered\newline(11)\newline11hr2727 mins\newlinex\newlineProgress saved\newlineSubmit and End\newlineQuestion 11\newline44 pts\newlineYou deposit $4000\$4000 in an account earning 5%5\% interest compounded monthly. How much will you have in the account in 1010 years?\newline$\$\newlineCheck Answer\newline58F58^\circ F\newlineMostly sunny\newlineSearch

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Q. Skills Quiz - Finance\newlineScore: 00/4040\newline00/1010 answered\newline(11)\newline11hr2727 mins\newlinex\newlineProgress saved\newlineSubmit and End\newlineQuestion 11\newline44 pts\newlineYou deposit $4000\$4000 in an account earning 5%5\% interest compounded monthly. How much will you have in the account in 1010 years?\newline$\$\newlineCheck Answer\newline58F58^\circ F\newlineMostly sunny\newlineSearch
  1. Identify Variables: First, identify the variables needed to calculate the future value of the investment:\newlinePrincipal amount PP = $4000\$4000\newlineAnnual interest rate rr = 5%5\% or 0.050.05\newlineNumber of times the interest is compounded per year nn = 1212 (monthly)\newlineNumber of years tt = 1010
  2. Convert to Monthly Rate: Convert the annual interest rate to a monthly interest rate by dividing by the number of times interest is compounded per year:\newlineMonthly interest rate r/nr/n = 0.05/120.05 / 12
  3. Calculate Monthly Rate: Calculate the monthly interest rate:\newlineMonthly interest rate = 0.0512=0.0041666667\frac{0.05}{12} = 0.0041666667
  4. Use Compound Interest Formula: Use the formula for compound interest to calculate the future value ( extit{A}): extit{A} = extit{P}(11 + extit{r}/ extit{n})^{( extit{nt})}
  5. Substitute Values: Substitute the values into the formula:\newlineA=4000(1+0.0041666667)(12×10)A = 4000(1 + 0.0041666667)^{(12 \times 10)}
  6. Calculate Exponent: Calculate the exponent part of the formula: nt=12×10=120n_t = 12 \times 10 = 120
  7. Calculate Future Value: Calculate the future value using the formula with all values substituted:\newlineA=4000(1+0.0041666667)120A = 4000(1 + 0.0041666667)^{120}
  8. Perform Calculation: Perform the calculation:\newlineA4000(1.0041666667)120A \approx 4000(1.0041666667)^{120}\newlineA4000×1.647009A \approx 4000 \times 1.647009\newlineA6588.036A \approx 6588.036

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