Question

Tina would like to withdraw an annual salary of $35,756 from an account paying 2.2% compounded annually for 35 years once she retires. Given this information, determine the amount needed in her account in order for her to reach her goal. Round to the nearest cent. I need to know what formula to use and how to input it into my calculator.

Answer 1

The formula for the present value of annuity(P) is given as,

`P=\text{PMT}*((1-((1)/((1+r)^n)))/(r))`

Given data

`\begin{gathered} P=Present\text{ value of annuity=?} \\ \text{PMT}=\text{Amount in each annuity payment(dollars)=\$35,756} \\ r=\text{discount rate=2.2\%=}\frac{\text{2.2}}{100}=0.022 \\ n=n\text{umber of payments left to receive}=35\text{years} \end{gathered}`

Hence,

`P=35,756*((1-((1)/((1+0.022)^(35))))/(0.022))`
`\begin{gathered} P=35,756*((1-((1)/((1.022)^(35))))/(0.022)) \\ P=35,756*((1-((1)/(2.141812027)))/(0.022)) \\ P=35756*((1-0.4668943807)/(0.022)) \\ P=35756*((0.5331056193)/(0.022)) \\ P=35756*(24.2320736) \\ P=866442.0238\approx866442.02(\text{nearest cent)} \end{gathered}`

Therefore,

`P(\text{Prevent value of annuity)=\$}866442.02`