Question

A 30 year annuity due earns a 6% rate of return.  If you invest $40,000, what is the payment (rounded to the nearest dollar) you will receive at the beginning of each year?

Answer 1

Given,

Present value = $40000

Rate of return (r) = 6% or 0.06

Term of annuity (n) = 30 years

Solution :-

Let payment be 'A'

Now,

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

$40000 = A/0.06 x [1 - (1 + 0.06)^-30] x (1 + 0.06)

$40000 = A/0.06 x [1 - (1.06)^-30] x (1.06)

$40000 = A/0.06 x [1 - 0.17411013091] x (1.06)

$40000 = A/0.06 x 0.82588986909 x 1.06

$40000 = A/0.06 x 0.87544326123

$40000 x 0.06/0.87544326123 = A

$2741 = A

So,

You will receive $2741 at the beginning of each year.