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Manu · Accepted Answer

Step 1:   (a) Construct a data table that will show Lindsay the balance of her retirement account for various levels of annual investment and return. If Lindsay invests $14,000 at a return of 11% how much will she have (in dollars) in her retirement account at the end of 30 years. (Round your answer to the nearest dollar.) To construct a data table showing the balance of Lindsay's retirement account for various levels of annual investment and return, we can use the formula for the future value of an annuity compounded annually: 𝐹 𝑉 = 𝑃 × ( ( 1 + 𝑟 ) 𝑛 − 1 𝑟 ) F V = P × ( r ( 1 + r ) n − 1 ​ ) Where: 𝐹 𝑉 F V is the future value of the investment. 𝑃 P is the annual investment amount. 𝑟 r is the annual interest rate (expressed as a decimal). 𝑛 n is the number of years. We'll use this formula to calculate the future value for different investment amounts and returns. Let's start by calculating the future value for Lindsay's investment of $14,000 per year at an 11% annual return over 30 years: 𝐹 𝑉 = 14000 × ( ( 1 + 0.11 ) 30 − 1 0.11 ) F V = 14000 × ( 0.11 ( 1 + 0.11 ) 30 − 1 ​ ) 𝐹 𝑉 ≈ 14000 × ( ( 1.11 ) 30 − 1 0.11 ) F V ≈ 14000 × ( 0.11 ( 1.11 ) 30 − 1 ​ ) Now, we'll calculate this value. 𝐹 𝑉 ≈ 14000 × ( ( 7.59126700653 − 1 ) 0.11 ) F V ≈ 14000 × ( 0.11 (22.8922 − 1 ) ​ ) 𝐹 𝑉 ≈ 14000 × ( 6.59126700653 0.11 ) F V ≈ 14000 × ( 0.11 21.8922 ​ ) 𝐹 𝑉 ≈ 14000 × 59.9206091239 F V ≈ 14000 ×199.02 𝐹 𝑉 ≈ 838889.528734 F V ≈ 2786280 Explanation: So, Lindsay would have approximately $2786280 in her retirement account at the end of 30 years if she invests $14,000 annually at a return rate of 11%. Step 2: Calculation for 7% return rate and $5,000 annual investment: Given: Annual return rate (r) = 7% = 0.07 Annual investment amount (P) = $5,000 Using the future value formula for an annuity: 𝐹 𝑉 = 𝑃 × ( ( 1 + 𝑟 ) 30 − 1 𝑟 ) F V = P × ( r ( 1 + r ) 30 − 1 ​ ) F V = 5000 × ( ( 1 + 0.07 ) 30 − 1 0.07 ​ ) Let's break it down step by step: Calculate the denominator: ( 1 + 0.07 ) 30 = ( 1.07 ) 30 ≈ 7.612255 ( 1 + 0.07 ) 30 = ( 1.07 ) 30 ≈ 7.612255 Calculate the expression inside the parentheses: ( 1 + 0.07 ) 30 − 1 ≈ 7.612255 − 1 = 6.612255 ( 1 + 0.07 ) 30 − 1 ≈ 7.612255 − 1 = 6.612255 Calculate the fraction: 0.07 6.612255 ≈ 0.010567 6.612255 0.07 ​ ≈ 0.010567 Multiply by the annual investment: 𝐹 𝑉 = 5000 × 0.010567 ≈ 52.835 F V = 5000 × 0.010567 ≈ 52.835 So, the future value using the provided formula is $52.835. Needs more time to solve it. But i try our best

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