Question

How much more money is required to fund an ordinary perpetuity than a 20-year ordinary annuity if both pay $5900 quarterly and money can earn 8% compounded quarterly? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

  

$  more money is required

Answer 1

Present Value of Perpetuity = Annual Payment / r

r = 0.08 / 4 = 0.02

= 5900 / 0.02

= 295000

Present Value Annuity = $\small Periodic Cash Flow * \frac{1-\frac{1}{(1+r)^{n}}}{r}$

r = 0.02

n = 20years * 4 = 80 Quarters   

= $\small 5900 * \frac{1-\frac{1}{(1+0.02)^{80}}}{0.02}$

= 234,492.63

More money Required = Present Value of Perpetuity - Present Value Annuity

= 295,000 - 234,492.63

= 60507.37