Question

An investment in a lease offers returns of ​$1000 per month due at the beginning of each month for four years. What investment is justified if the returns are deferred for two years and the interest required is 4​% compounded quarterly​?

Answer 1

ANSWER DOWN BELOW. FEEL FREE TO ASK ANY DOUBTS. THUMBS UP PLEASE.

Part 1:

Formula: The present value of an annuity due (PV)

PV = {C× [1-(1+r)^-n]/r}×(1+r)}

PV = Present value (The cumulative amount available at Present).
C= Periodic cash flow. 1000
r =effective interest rate for the period. [(1.01)^(1/3)]-1= 0.33223% or 0.0033223
n = number of periods. 4*12=48

PV = {1000× [1-(1+0.0033223)^-48]/0.0033223}×(1+0.0033223)}

PV = $44,447.65

Present value of all lease payment = $44,447.65

Part 2: if it is differed by 2 years:

Formula:
Future value= present value(1+r)^n

r= interest rate for the period. [(1.01)^(4)]-1= 4.06%
n = number of periods. 2

FV = $44,447.65*(1+0.0406)^2

FV =$48,130.44

The investment that is justified if the returns are deferred for two years is $48,130.44