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The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. Answer parts (a) and (b).\newline\newlinePrincipal\newlineRate\newlineCompounded\newlineTime\newline\newline$1500\$1500\newline22.22\%\newlinedaily\newline33.55 years\newline\newlineQuestion 33\newlineQuestion 44\newlinea. Find how much money there will be in the account after the given number of years. (Assume 365365 days in a year.)\newlineThe amount of money in the account after 33.55 years is \newline$□\$\square,\newline(Round to the nearest cent as needed.)\newlineMedia 22\newlineQuestion 55\newlineMedia 33\newlineQuestion 66\newlineQuestion 77

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Q. The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. Answer parts (a) and (b).\newline\newlinePrincipal\newlineRate\newlineCompounded\newlineTime\newline\newline$1500\$1500\newline22.22\%\newlinedaily\newline33.55 years\newline\newlineQuestion 33\newlineQuestion 44\newlinea. Find how much money there will be in the account after the given number of years. (Assume 365365 days in a year.)\newlineThe amount of money in the account after 33.55 years is \newline$□\$\square,\newline(Round to the nearest cent as needed.)\newlineMedia 22\newlineQuestion 55\newlineMedia 33\newlineQuestion 66\newlineQuestion 77
  1. Identify formula for compound interest: Identify the formula for compound interest.\newlineThe formula for compound interest is A=P(1+rn)ntA = P(1 + \frac{r}{n})^{nt}, where:\newlineAA = the amount of money accumulated after nn years, including interest.\newlinePP = the principal amount (the initial amount of money).\newlinerr = the annual interest rate (decimal).\newlinenn = the number of times that interest is compounded per year.\newlinett = the time the money is invested for, in years.
  2. Convert interest rate to decimal: Convert the annual interest rate from a percentage to a decimal.\newlineTo convert the rate from a percentage to a decimal, divide by 100100.\newlineRate (r)=2.2%=2.2100=0.022(r) = 2.2\% = \frac{2.2}{100} = 0.022
  3. Determine values for PP, rr, nn, tt: Determine the values for PP, rr, nn, and tt.\newlinePrincipal (PP) = $1500\$1500\newlineRate (rr) = rr11 (from Step 22)\newlineCompounded (nn) = rr33 (since it is compounded daily)\newlineTime (tt) = rr55 years
  4. Calculate amount using formula: Calculate the amount of money AA using the compound interest formula.A=1500(1+0.022365)365×3.5A = 1500(1 + \frac{0.022}{365})^{365 \times 3.5}
  5. Perform calculations inside parentheses: Perform the calculations inside the parentheses first.\newlineCalculate 1+rn1 + \frac{r}{n}:\newline1+0.022365=1+0.00006027397≈1.000060273971 + \frac{0.022}{365} = 1 + 0.00006027397 \approx 1.00006027397
  6. Calculate exponent: Calculate (n×t)(n \times t), which is the exponent.365×3.5=1277.5365 \times 3.5 = 1277.5
  7. Raise result to power: Raise the result from Step 55 to the power of the result from Step 66.\newline(1.00006027397)1277.5(1.00006027397)^{1277.5}\newlineThis calculation requires a calculator.
  8. Multiply principal for final amount: Multiply the principal by the result from Step 77 to find the final amount.\newlineA=1500×(1.00006027397)1277.5A = 1500 \times (1.00006027397)^{1277.5}\newlineAgain, this calculation requires a calculator.
  9. Use calculator for computation: Use a calculator to compute the final amount.\newlineA=1500×(1.00006027397)1277.5≈1500×1.080947576A = 1500 \times (1.00006027397)^{1277.5} \approx 1500 \times 1.080947576\newlineA≈1500×1.080947576≈1621.42A \approx 1500 \times 1.080947576 \approx 1621.42
  10. Round result to nearest cent: Round the result to the nearest cent.\newlineThe amount of money in the account after 3.53.5 years is approximately $1621.42\$1621.42.

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