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Jason deposits $830 every month into an account earning an annual interest rate of 3.9% compounded monthly. How much would he have in the account after 9 months, to the nearest dollar? Use the following formula to determine your answer. A=d(((1+i)^(n)-1)/(i)) A= the future value of the account after n periods d= the amount invested at the end of each period i= the interest rate per period n= the number of periods Answer:

Jason deposits $830 \$ 830 every month into an account earning an annual interest rate of 3.9% 3.9 \% compounded monthly. How much would he have in the account after 99 months, to the nearest dollar? Use the following formula to determine your answer.\newlineA=d((1+i)n−1i) A=d\left(\frac{(1+i)^{n}-1}{i}\right) \newlineA= A= the future value of the account after n n periods\newlined= d= the amount invested at the end of each period\newlinei= i= the interest rate per period\newlinen= n= the number of periods\newlineAnswer:

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Q. Jason deposits $830 \$ 830 every month into an account earning an annual interest rate of 3.9% 3.9 \% compounded monthly. How much would he have in the account after 99 months, to the nearest dollar? Use the following formula to determine your answer.\newlineA=d((1+i)n−1i) A=d\left(\frac{(1+i)^{n}-1}{i}\right) \newlineA= A= the future value of the account after n n periods\newlined= d= the amount invested at the end of each period\newlinei= i= the interest rate per period\newlinen= n= the number of periods\newlineAnswer:
  1. Identify Values: Identify the given values from the problem.\newlineJason deposits $830\$830 every month into an account, so d=$830d = \$830.\newlineThe annual interest rate is 3.9%3.9\%, so the monthly interest rate i=3.9%12 months=0.325%i = \frac{3.9\%}{12 \text{ months}} = 0.325\% per month.\newlineThe number of periods n=9n = 9 months.
  2. Convert Interest Rate: Convert the annual interest rate to a decimal to use in the formula.\newlinei=3.9%100=0.039i = \frac{3.9\%}{100} = 0.039 (annual rate in decimal)\newlinei=0.03912i = \frac{0.039}{12} (monthly rate in decimal)\newlinei≈0.00325i \approx 0.00325
  3. Plug into Formula: Plug the values into the compound interest formula to calculate the future value AA.A=d×((1+i)n−1)/iA = d \times \left(\left(1 + i\right)^{n} - 1\right) / iA=830×((1+0.00325)9−1)/0.00325A = 830 \times \left(\left(1 + 0.00325\right)^{9} - 1\right) / 0.00325
  4. Calculate Exponent: Calculate the value inside the parentheses and the exponent.\newline(1+0.00325)9≈1.02947(1 + 0.00325)^{9} \approx 1.02947
  5. Subtract One: Continue the calculation by subtracting 11 from the result of the exponentiation.\newline1.02947−1≈0.029471.02947 - 1 \approx 0.02947
  6. Divide by Rate: Divide the result by the monthly interest rate ii.\newline0.02947/0.00325≈9.067690.02947 / 0.00325 \approx 9.06769
  7. Multiply by Deposit: Multiply the result by the monthly deposit amount dd to find the future value AA.A=830×9.06769A = 830 \times 9.06769A≈7526.2027A \approx 7526.2027
  8. Round to Nearest Dollar: Round the future value AA to the nearest dollar.A≈$(7526)A \approx \$(7526)

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