Question

A perpetuity will make annual payments with the first payment coming 9 years from now. The first payment is for $4700, and each payment that follows is $150 dollars more than the previous one. If the effective rate of interest is 6.2%, what is the present value of the perpetuity?

Answer = $

Answer 1

A perpetuity is the fixed periodic payments made indefinitely. For example a irredeemable preference shares gives investors dividend indefinitely. This is perpetuity. To calculate growing perpetuities which is occurring indefinitely,

P= A/(i-g)

Where, P is present value of the perpetuity

A is first amount received of perpetuity

i is the rate of interest and g is the rate of growing perpetuity

Now, here percentage growth of perpetuity is = 150/4200 = 3.571%

So P= 4700/(.0620- .0357) = $ 178,707.227

Hence the present value of perpetuity is $178,707.227