Respuesta :
The amount Beth would be able to withdraw quarterly from her inheritance over the next 20 years is Quarterly Payments ≈ $11,124.53
The given parameters in the question;
Present value of inheritance, PV = $500,000
The number of years of withdrawal, n = 20 years
Interest rate, i = 6.4%
The required parameter;
The amount Beth would be able to withdraw quarterly over the next 20 years to draw the account down to zero, given a quarterly interest rate of 6.4%
Method
The required parameter is given by the payment formula
The question is related with annuity given that withdrawals will be made quarterly
The question seeks to find how much she can withdraw so as to exhaust the balance in 20 years
The amount she can withdraw quarterly is given by the payment formula as follows;
[tex]\mathbf{PMT = PV \times \dfrac{i}{1 - \left(1 + i\right)^{-n}}}[/tex]
Where;
PMT = The amount of quarterly payments
PV = The present value of the investment = $500,000
i = The interest rate = 6.4%
n = The number of years = 20 years
Therefore, we get;
[tex]\mathbf{PMT = 500,000 \times \dfrac{\dfrac{0.064}{4} }{1 - \left(1 + \dfrac{0.064}{4} \right)^{-4 \times 20}} \approx 11,124.53}[/tex]
The amount she can withdraw quarterly for the next 20 years ≈ $11,124.53
Quarterly payment, PMT = $11,124.53
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