Question

Your parents will retire in 20 years. They currently have $300,000 saved, and they think they will need $1,450,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds?

Answer 1

N=20 periods (years)
present value, P = 300,000
future value, F= 1450000
i=annual interest rate

$F=P(1+i)^n$
$1450000=300000(1+i)^{20}$
$(1+i)^{20}=1450000/300000$
$(1+i)^{20}=29/6$
$(1+i)=(29/6)^{1/20}$
$i=(29/6)^{1/20}-1$
$i=(29/6)^{1/20}-1$
$=1.081963-1$
$=0.081963$
$=8.1963%$

Answer: they need to earn 8.1963% or more to achieve their goal.