Question

Three years from now you will begin receiving annual payments of? $7,200. this will continue for 14 years. at a discount rate of? 5.8%, what is the present value of this stream of cash? flows?

Answer 1

The cash flow is considered to be a deferred one because the annual payments is made on a later date. The formula for finding the present value (PV) of a deferred annuity is given as:

PV of annuity = A * ((1 - (1 + i)^-n)/ i) (1 + i)^-k

Where,

A = annual payments = 7,200

i = interest rate = 5.8% = 0.058

n = number of years = 14

k = deferred years = 3

Substituting the given values into the formula:

PV = 7,200 * [(1 – (1 + 0.058)^-14) / 0.058] (1 + i)^-3

PV = 57,216.29

Therefore the present value is about $57,216.29

Answer 2

The type of annuity presented above is a deferred annuity because the payment starts sometime in the future. The present worth of deferred annuity is calculated through the equation,

PV = R x ((1 - (1 + i)^-n)/ i) (1 + i)^-k

where PV is the present worth
R is payment = $7200
n is the total number of payments to be made = 14
k is the deferred period = 3
i is interest = 0.058

Substituting the known values,
PV = ($7,200) ((1 - (1 + 0.058)^-14) / 0.058)(1 + 0.058)^(-3)
PV = $57,216

Thus, the present worth of the deferred annuity is approximately $57,216.3.