Siri plans to retire when her simple annuity savings account has enough money to receive $10 000.00 per month for twenty years starting at the start of the first month after her retirement. She starts saving $4420 per month. Calculate when should Siri retire from today if her savings account pays 4.9% compounded monthly.

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To determine when Siri can retire, we need to calculate two main components: the future value of her annuity savings and the present value of the annuity she desires at retirement.1. **Future Value of Savings**: This is the amount Siri will have saved up by the time she retires. The formula for the future value of an annuity is $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $P$ is the payment amount, $r$ is the monthly interest rate, and $n$ is the total number of payments.Given:- Monthly savings ($P$) = $4420- Annual interest rate = 4.9%, so the monthly interest rate ($r$) = 4.9% / 12 = 0.004075- We're solving for $n$, the number of months until retirement.2. **Present Value of Desired Retirement Annuity**: This is the amount needed at the start of retirement to ensure Siri can withdraw $10,000 per month for 20 years. The formula for the present value of an annuity is $PV = P \times \frac{1 - (1 + r)^{-n}}{r}$.Given:- Monthly withdrawal ($P$) = $10,000- $n$ = 20 years * 12 months/year = 240 months- $r$ = 0.004075First, calculate the present value (PV) needed at retirement:$$PV = 10,000 \times \frac{1 - (1 + 0.004075)^{-240}}{0.004075} \approx 1,713,485.77$$Next, solve for $n$ in the future value formula where $FV = PV$:$$1,713,485.77 = 4420 \times \frac{(1 + 0.004075)^n - 1}{0.004075}$$Solving this equation for $n$ gives a value of approximately 216 months, or 18 years.Therefore, Siri should retire in 18 years to meet her retirement goals.

Siri Plans to Retire When Her Simple Annuity Savings Account