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Layla is saving money and plans on making monthly contributions into an account earning an annual interest rate of 5.7% compounded monthly. If Layla would like to end up with $113,000 after 14 years, how much does she 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:

Layla is saving money and plans on making monthly contributions into an account earning an annual interest rate of 5.7% 5.7 \% compounded monthly. If Layla would like to end up with $113,000 \$ 113,000 after 1414 years, how much does she 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. Layla is saving money and plans on making monthly contributions into an account earning an annual interest rate of 5.7% 5.7 \% compounded monthly. If Layla would like to end up with $113,000 \$ 113,000 after 1414 years, how much does she 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 values: Identify the given values from the problem.\newlineAA (future value of the account) = $113,000\$113,000\newlineii (monthly interest rate) = 5.7%5.7\% annual interest rate / 1212 months = 0.04750.0475 per month\newlinenn (total number of periods) = 1414 years * 1212 months/year = 168168 months\newlineNow, we will use these values in the formula provided.
  2. Convert interest rate: Convert the annual interest rate to a monthly interest rate. i=5.7%per year/100i = \frac{5.7\%}{\text{per year}} / 100 (to convert percentage to a decimal) /12/ 12 months =0.00475= 0.00475 per month
  3. Calculate periods: Calculate the number of periods nn.n=14 years×12 months/year=168 monthsn = 14 \, \text{years} \times 12 \, \text{months/year} = 168 \, \text{months}
  4. Plug values into formula: Plug the values into the formula to solve for dd (the monthly contribution).A=d×((1+i)n−1i)A = d \times \left(\frac{(1 + i)^{n} - 1}{i}\right)(\newline\)$113,000=d×((1+0.00475)168−10.00475)\$113,000 = d \times \left(\frac{(1 + 0.00475)^{168} - 1}{0.00475}\right)
  5. Calculate inside parentheses: Calculate the value inside the parentheses.\newline(1+0.00475)168−1(1 + 0.00475)^{168} - 1\newline= (1.00475)168−1(1.00475)^{168} - 1\newline= 2.113114545−12.113114545 - 1\newline= 1.1131145451.113114545
  6. Divide by interest rate: Divide the result by the monthly interest rate.\newline1.1131145450.00475=234.3409579\frac{1.113114545}{0.00475} = 234.3409579
  7. Solve for monthly contribution: Solve for dd (the monthly contribution).\newline$113,000=d×234.3409579\$113,000 = d \times 234.3409579\newlined=$113,000234.3409579d = \frac{\$113,000}{234.3409579}\newlined≈$482.12d \approx \$482.12
  8. Round monthly contribution: Round the monthly contribution to the nearest dollar. d≈$482d \approx \$482

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