Question

if you put up 41,940 in exchange for a 8.6 percent, 12 year annuity what will the annual cash flow be (round time value factors to 6 decimal places and final to nearest dollar)

Answer 1

The given stream of cash flows represents an annuity and the present value of the annuity is given. So, we have to use the equation of present value of annuity and calculate the annuity receivable each year

Present value of annuity = P x [ 1 – ( 1 + r ) ^ - n ] / r

Where,

Present value of annuity = $ 41,940

P = Annuity each year

r = Rate of Interest = 8.6% or 0.086

n = Years = 12

So, putting the values in above equation

$ 41,940 = P x [ 1 – 1.086 ^ - 12 ] / 0.086

So, $41,940 = P x [ 1 - 0.371571 ] / 0.086

So, $41,940 = P x 0.628429/ 0.086

So, $41,940 = P x 7.307314

So, P = $41,940 / 7.307314

= $5,739