Question

A piece of furniture costs $2500. You can buy it now with cash or pay an amount of $3000 in 3 years.

(a) At compound interest rate of 10% annually, which option should you choose?

(b) At what compound effective annual rate, the two options are the same to you?

Answer 1

a.Present value of amount payable in 3 years=Cash flow*Present value of discounting factor(rate%,time period)

=3000/1.1^3

=3000*0.751314801

=$2253.94(Approx)

Hence $3000 in 3 years is better option having lower present value

b.We use the formula:  
A=P(1+r/100)^n
where   
A=future value
P=present value  
r=rate of interest
n=time period.

3000=2500*(1+r/100)^3

(3000/2500)^(1/3)=(1+r/100)

(1+r/100)=1.0627

r=1.0627-1

=6.27%(Approx)