Question

6. What is the present value of $2,625 per year at a discount rate of 8%, if the first payment is received six years from now and the last payment is received 20 years from now

Answer 1

PV ( in year 0 terms) = $15,291.77

Step-by-step explanation:

An annuity starting in six years time and ends 20 years from now would give 15 annual cash inflows.

The present value of such annuity would be calculated in two (2) steps as follows:

Step 1: PV of annuity (in year 5 terms)

PV of annuity (in year 5 terms)= A× (1- (1+r)^(-n) )/r

A-2,625, r- 8%, n-15

PV = 2,625, × (1- (1+0.08)^(-15))/0.08= 22,468.632

Step 2:PV ( in year 0 terms)

PV ( in year 0 terms) = FV × (1+r)^(-n)

FV- 2,468.632, r-8%, n-5

PV = 2,468.632 × 1.08^(-5) = 15,291.7731

PV ( in year 0 terms) = $15,291.77

Present Value = $15,291.77