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

Please Discuss in case of Doubt

Best of Luck. God Bless

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