Answer to Question #123065 in Financial Math for shimran

Question

What annual deposits are needed for 10 years to provide for a perpetuity of $3000 per year with the 1st payment due at the end of 11, 1 year after the final deposit with J1 = 8% p.a.?

Answer 1

The value of perpetuity at the end of 10 years = yearly payment/rate

I=8%per annum

PV = 3000 / 0.08

PV = $ 37,500.00

The Future value of annuity F = $37,500

rate r = 8%

time t = 10 years

annual payment C=?

F = (C/r)*((1+r)^t-1)

37500 = (C/0.08)*((1+8%)¹⁰ -1)

C*(1.08¹⁰-1) = 37500*0.08

C*1.16 = 3000

Annual payments (C )= $2,588.61