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Find the annual payment required to save $50,000 after 6 years,

if you place the money in an account paying 4% per annum compounded
annually.
please show all steps! thank you!

1 Answer

3 votes

Answer: $7,107.47

Step-by-step explanation: To find the annual payment required to save $50,000 after 6 years with a 4% annual interest rate compounded annually, you can use the formula for the future value of an ordinary annuity. The formula for the future value of an ordinary annuity is: FV = P * ((1 + r)^n - 1) / r Where: FV is the future value P is the annual payment r is the interest rate per compounding period n is the number of compounding periods In this case, the future value (FV) is $50,000, the interest rate (r) is 4% or 0.04, and the number of compounding periods (n) is 6. Let's plug in the values into the formula and solve for the annual payment (P): $50,000 = P * ((1 + 0.04)^6 - 1) / 0.04 To solve for P, we can multiply both sides of the equation by 0.04: $50,000 * 0.04 = P * ((1 + 0.04)^6 - 1) $2,000 = P * (1.04^6 - 1) Next, we can simplify the equation by calculating the value of (1.04^6 - 1): (1.04^6 - 1) ≈ 0.2814 Now, we can divide both sides of the equation by 0.2814 to solve for P: $2,000 / 0.2814 ≈ P P ≈ $7,107.47 Therefore, the annual payment required to save $50,000 after 6 years, with a 4% annual interest rate compounded annually, is approximately $7,107.47.

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