Question

What amount must be set aside now to generate payments of $50,000 at the beginning of each year for the next 12 years if money is worth 5.84%, compounded annually? (Round your answer to the nearest cent.)

Answer 1

Answer

We must set aside amount equal to that Net Present of all future amount.

Present Value of a periodic payment when payment is made at the end of the years are given by :

PV = (P/r)(1 - 1/(1 + r)ⁿ)

where PV = Present Value, P = periodic payment = 50,000, r = interest rate = 5.84% = 0.0584, n = time period = 11(Note this formula is form end of year payment and thus there are 11 end of year payment and first payment is the current payment and thus we will just add this 50,000 to above calculated Present value to get the exact value of this Net Present worth).

Thus PV = (50,000/0.0584)(1 - 1/(1 + 0.0584)¹¹) = 397590.82

Thus Net Present Value = 397590.82 + Payment at the beginning of year 1 = 397590.82 + 50,000 = 447590.82

Hence , We must set aside now amount $447590.82.