Question

9. 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: $4500 Interest rate: 4.5% Frequency quarterly Time: 24 years Account balance: $

Answer 1

This is a question on Future Value of Annuity. There is a present sum from which withdrawals will be made. We therefore employ the formulae thus:

`PVA=\text{PMT(}(1-(1+(i)/(m))^(-mn))/((i)/(m))\text{)}`

Where:

PVA = Present Value of Annuity

PMT = Periodic sum

i = Interest Rate

n = Number of interest periods

m = Compunding frequency

Substituting, we have:

`\begin{gathered} P\text{VA}=4500((1-(1+(0.045)/(4))^(-(4*24)))/((0.045)/(4))) \\ P\text{VA}=263,340 \end{gathered}`

PVA = $263,340