4-58. Lisa plans to retire on her 61st birthday. On her
22nd birthday, Lisa will start saving SA per year for
40 years. Starting on her 62nd birthday, Lisa plans on
withdrawing $10,000 and will continue these annual
withdrawals until the account is exhausted on her 85th
birthday. If Lisa's bank account pays 3% per year, what
annual amount of SA will Lisa need to invest in her bank
account to achieve her retirement goal? (4.10)​

Respuesta :

Answer:

Lisa invest "$2180.81" in her bank.

Step-by-step explanation:

The given values are:

On Lisa's 62nd birthday,

she withdraw = $10,000

The annuity of $A will remain at 3 percent for 40 years. The retirement pension of $10000 lasts 23 years at rate percentage of 3 but begins 40 years later.

⇒  [tex]A\times (\frac{P}{A} ,3 \ percent,40) - 10000 (\frac{P}{A} ,3 \ percent,23)\times \frac{1}{(1.03)40} = 0[/tex]

⇒  [tex]A\times 23.1148 - 10000\times 16.4436\times 0.3066 = 0[/tex]

⇒  [tex]A = 10000\times 16.4436\times \frac{0.3066}{23.1148}[/tex]

⇒      [tex]= 10000\times 16.4436\times 0.0132[/tex]

⇒      [tex]=2180.81[/tex] ($)