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Malik is saving money and plans on making monthly contributions into an account earning a monthly interest rate of 0.65%. If Malik would like to end up with $8,000 after 18 months, how much does he need to contribute to the account every month, 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:

Malik is saving money and plans on making monthly contributions into an account earning a monthly interest rate of 0.65% 0.65 \% . If Malik would like to end up with $8,000 \$ 8,000 after 1818 months, how much does he need to contribute to the account every month, 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. Malik is saving money and plans on making monthly contributions into an account earning a monthly interest rate of 0.65% 0.65 \% . If Malik would like to end up with $8,000 \$ 8,000 after 1818 months, how much does he need to contribute to the account every month, 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 Variables: Identify the variables from the problem.\newlineAA (future value of the account) = $8,000\$8,000\newlineii (interest rate per period) = 0.65%0.65\% per month or 0.00650.0065 in decimal form\newlinenn (number of periods) = 1818 months\newlineWe need to find dd (the amount invested at the end of each period).
  2. Convert Interest Rate: Convert the interest rate from a percentage to a decimal.\newline0.65%=0.65100=0.00650.65\% = \frac{0.65}{100} = 0.0065
  3. Plug Values into Formula: Plug the values into the formula to solve for dd.A=d×((1+i)n−1i)A = d \times \left(\frac{(1 + i)^{n} - 1}{i}\right)(\newline\)$8,000=d×((1+0.0065)18−10.0065)\$8,000 = d \times \left(\frac{(1 + 0.0065)^{18} - 1}{0.0065}\right)
  4. Calculate (1+i)n(1 + i)^{n}: Calculate the value of (1+i)n(1 + i)^{n}.(1+0.0065)18=(1.0065)18(1 + 0.0065)^{18} = (1.0065)^{18}
  5. Evaluate Exponent: Evaluate the exponent.\newline(1.0065)18≈1.1213(1.0065)^{18} \approx 1.1213 (rounded to four decimal places for simplicity)
  6. Substitute Value: Substitute the value from Step 55 into the formula.\newline$8,000=d×(1.1213−10.0065)\$8,000 = d \times \left(\frac{1.1213 - 1}{0.0065}\right)
  7. Calculate Numerator: Calculate the numerator of the fraction.\newline1.1213−1=0.12131.1213 - 1 = 0.1213
  8. Divide by Interest Rate: Divide the numerator by the interest rate.\newline0.1213/0.0065≈18.66150.1213 / 0.0065 \approx 18.6615
  9. Solve for d: Solve for d by dividing the future value AA by the result from Step 88.\newlined=extextdollar8,00018.6615d = \frac{ ext{ extdollar}8,000}{18.6615}
  10. Calculate Contribution: Calculate the monthly contribution. d≈$(428.88)d \approx \$(428.88)
  11. Round to Nearest Dollar: Round the monthly contribution to the nearest dollar. d≈$429d \approx \$429 (to the nearest dollar)

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