Question

You are 20 years old and you want to have $1,500,000 by the time you are 62 years old.  You believe by putting money in the stock market you can earn 7.8% return.  How much should you put in each year to reach this goal?

At age 65 you will receive an annuity of $1,200 a month, and you expect to live until 85.  If you are 28 years old today, how much is that Annuity worth today?  At a rate of 5.6%

You want to retire and believe you will need $3,300 a month to live on for the next 25 years.  How much will you need to invest today to have the $3,300 per month?   At a rate of 7.7%

You win the lottery for $30,000,000 but you have to take it in 20 payments.  An outside company will offer you to give you a lump sum up front.  You believe you can earn 5.6% on the money, what amount would you accept.

Answer 1

1. Number of years = 42
FV = 1,500,000
Rate =7.8%
Using future value of annuity
FV = PMT*((1+r)ⁿ-1)/r
Amount to be put each year PMT = 1,500,000/((1+7.8%)⁴²-1)/7.8% =  5212.79

2. Number of periods from 65 to 85 = 20*12 = 240
Rate per month = 5.6%/12
Value of Amount at age 65 using annuity formula = 1200*(1-(1+5.6%/12)^-240)/(5.6%/12) = 173,023.47
Value of of all annuity at age 28 = 173,023.47/(1+5.6%)³⁷ = 23043.05


3. Number of periods = 12*25 =300
Rate per month = 7.7%/12
Present value using annuity formula = 3300*((1-(1+7.7%/12)^-300)/(7.7%/12) = 438,801.11

4. Per year amount received = 30,000,000/20 = 1,500,000
Rate = 5.6%
PV = 1,500,000*(1-(1+5.6%)^-20)/5.6% = 17,777,787.08

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