Q1.Answer:
For a PEA to be worthwhile, its present value to you now must be at least $25,000. In 10 years, the PEA will be worth $50,000, and its present value to you now is $50,000/(1 + r) 10, where r is your personal discount rate. Thus,
$50,000/ (1+r) 10 = $25,000 or
$50,000/$25,000 = (1+r) 10
2 = (1+r) 10
(1+r) = (2)1/10
(1+r) = 1.0718
r = 0.0718
Your personal discount rate needs to be 7.18% or less for the PEA to be worth investing in.
Q2. Answer:
This is annuity due
Fv = PV× ((1+r) ^t) – 1/r) × (1+r)
So 150 × (1+10/12^25×12))-1)/0.10/12 × (1+10/12) =$200,683.5522.
Yes the worker will have $200,000 at the end of the 25 years if he will be contributing 150 per year.
Q3.Answer
FV = PV * (1+i) ^n.
Therefore,
= (468,000 = 136,000 × (1.08) ^t)
= (468,000 ÷ 136,000 = ((136,000) × (1.08) ^t)) ÷ 136,000)
= (3.441176471 = (1.08) ^t)
= (ln3.441176471÷ ln1.08 = T so T = 9.3608817%
Q4. Answer
FV = PV * (1+i) ^n.
Therefore,
= (392,000 = 112,000 × (1+R) ^14)
= (392,000 ÷ 112,000 = ((112,000) × (1+R) ^14)) ÷ 112,000)
= 3.5(1/14) = (1+R) ^ (14×1/14) =14 √3.5 -1) = R
= so R = 9.3608817%
