Question

How much money do you need on March 30, 2014 earning 9% compounded quarterly in order to withdraw $350 every quarter with the first withdrawal on June 30, 2014 and the last withdrawal made on December 30, 2045?

Answer 1

First, let us find the number of quarters in the given plan.

From March 30, 2014, to March 30, 2045, is 31 years, and from March 30 2045 to December 30, 2045, there are 3 quarters.

Therefore, Total quarters = (31 * 4) + 3 = 127 quarters

Quarterly interest rate = 9% / 4 = 2.25%

Now we can use "the present value of the annuity regular" formula to find the amount we need today.  

Where,
PVA = Present value of the annuity
A = Annuity or payment
i = Interest rate in decimal form (2.25% = 0.0225)
n = Number of quarters

Therefore, the money you need on March 30, 2014, is $14,633.74