Question

Question: Betty Bronson has just retired after 25 years with the electric company. Her total pension funds have an accumulated value of $180,000, and her life expectancy is 15 more years. Her pension fund manager assumes he can earn a 9 percent return on her assets. What will be her yearly annuity for the next 15 years?

Short answer

Answer

The yearly annuity will be $22,330.60.

Step-by-step solution

Identification of the required information

Present value (PV) = $180,000

Periods (n) = 15

Interest rate (i) = 9%

Computation of the yearly annuity (PMT)

$$\begin{gathered} \mathit{P}\mathit{V}\mathbf{=}\mathit{P}\mathit{M}\mathit{T}\mathbf{\times }\left[\frac{1-{\left(1+i\right)}^{-n}}{i}\right] \\ \mathbf{\$}\mathbf{180}\mathbf{,}\mathbf{000}\mathbf{=}\mathit{P}\mathit{M}\mathit{T}\mathbf{\times }\mathbf{\left[}\frac{\mathbf{1}\mathbf{-}{\left(1+9\%\right)}^{\mathbf{-}\mathbf{15}}}{\mathbf{9}\mathbf{\%}}\mathbf{\right]} \\ \mathit{P}\mathit{M}\mathit{T}\mathbf{=}\mathbf{\$}\mathbf{22}\mathbf{,}\mathbf{330}\mathbf{.}\mathbf{60} \end{gathered}$$