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Q1. Prepaid college tuition plans, also known as Prepaid Education Arrangements (PEAs), allow you to prepay college tuition at present-day prices. The value of the investment is guaranteed by the stat
Q1. Prepaid college tuition plans, also known as Prepaid Education Arrangements (PEAs), allow you to prepay college tuition at present-day prices. The value of the investment is guaranteed by the state to cover college tuition, regardless of its future cost. You are considering the purchase of an education certificate for $25,000, which will cover the future tuition costs of your 8-year old daughter. You expect the tuition cost of your daughter’s bachelor’s degree to be $50,000 in 10 years. What would your personal discount rate need to be in order for it to be worthwhile for you to make the investment and purchase the certificate?
Q2. A 30 year old employee hopes to have $200,000 saved in their retirement account 25 years from now by contributing $150 per month in a 401(k) plan. The goal is to earn 10% annually on the monthly contribution. Will they have the $200,000 at the end of the 25 years?
Q3. How many years will it take for $136,000 to grow to $468,000 if it is invested in an account with an annual interest rate of 8%?
Q4. At what interest rate must $112,000 be invested so that it will be worth $392,000 in 14 years?
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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%