11. You expect to have the given amount in an account with the given terms. Find how much you can withdraw periodically in order

Question

1 year ago

6

11. You expect to have the given amount in an account with the given terms. Find how much you can withdraw periodically in order

to make the account last the specified amount of time. Round your answer to the nearest cent. Account balance: $300,000 Interest rate: 4.45% Frequency daily Time: 22 years Regular withdrawal amount: $

Mathematics

1 answer:

Orlov [11] · Answer 1 · 2024-09-09T01:36:14+03:00

Orlov [11]1 year ago

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This is a question on Present Value of Annuity and we seek the periodic withdrawal.

$\begin{gathered} F\text{VA}=\text{PMT(}\frac{(1+\frac{i}{m})^{nm}-1}{\frac{i}{m}}) \\ \text{Therefore, PMT=}\frac{FVA}{(\frac{(1+\frac{i}{m})^{nm}-1}{\frac{i}{m}})} \end{gathered}$

where:

FVA = Future value of annuity

PMT = Periodic Withdrawal

i = interest/discount rate

n = no of years

m = no of compundings per interest period

$\text{PMT=}\frac{300000}{(\frac{(1+\frac{0.0445}{365})^{22\times365}-1}{\frac{0.0445}{365}})}=22.01$

PMT = $22.01