Question

How much money is required now to provide an income of $1,600 per month for six years if the money earns interest at 6% p.a. compounding monthly and the first $1,600 payment is payable 2 years from today?

Answer 1

Present value of annuity due = p*[1 - (1+r)^-n / r]*(1+r)

(Above present value is at T = 2 (i.e., in year 2)

p = monthly income = 1600

r = rate of interest per period = 6% / 12 = 0.5%

n = number of periods = 6*12 = 72

Present value = 1600*[1 - (1+0.5%)^-72 / 0.5% ]*(1+0.5%)

Present value(at T = 2) = $97,025.94

Present value(at T = 0) = future value / (1+r)^n

r = rate of interest = 0.5%

n = number of periods = 24 months

Present value = 97,025.94 / (1+0.5%)^24

= $86,080.02

So we required $86,080.02 today