Answered

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7. You want to be able to withdraw the specified amount periodically from a payout annuity with the given terms. Find how much the account needs to hold to make this possible. Round your answer to the nearest dollar. Regular withdrawal: $2100 Interest rate: 2% Frequency weekly Time: 19 years Account balance: $

7 You Want To Be Able To Withdraw The Specified Amount Periodically From A Payout Annuity With The Given Terms Find How Much The Account Needs To Hold To Make T class=

Sagot :

Use the payout annuity formula.

[tex]P_0=\frac{d(1-(1+\frac{r}{k})^{-Nk})}{(\frac{r}{k})}[/tex]

The weekly withdrawl is $2100 so d=$2100

Each year has around 52 weeks so number of periods is k=52.

The interest rate is 2% per annum so r=0.02

The number of years is 19 so N=19.

So it follows:

[tex]\begin{gathered} P_0=\frac{2100(1-(1+\frac{0.02}{52})^{-19\times52})}{\frac{0.02}{52}} \\ P_0=1725843.905 \end{gathered}[/tex]

Hence you should have $1725843.905 in your bank account to pay yourself $2100 a week for 19 years if the account earns 2% per annum.

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