What is meant bu the time value of money: Note that, the annualized return for U

Question

What is meant bu the time value of money: Note that, the annualized return for U.S. large-company stocks (as represented by Standard & Poor's 500-stock index) for the past 75 years has been about 10%, not including taxes. Say your goal is to build a nest egg of $1 million by the time you are 55. If you start at age 24 and invest $5,000 a year at an annualized return of 10%, you'll reach your goal. But if you wait until you are 34 to start, you'll accumulate only $357,000 by age 55. If you start at age 44, you'll have just $107,000. Here's a second example, even more dramatic. Karen begins at age 25 to put $2,000 a year into a low-expense mutual fund with an annualized return of 10%. At age 35, she put $20,000 into the fund. Then she stops investing entirely. But the value of Karen's holdings keeps rising, and by the time he is 65, he has a portfolio that is worth $556,000. (We are assuming this is a tax-deferred account, such as a 401(k) or an IRA.) Do you agree/disagree? WHY:

Explanation / Answer

Time value of money is the effect of compounding of money. The value of money needs to increase over time to protect from the effect of inflation. Investors also want some additional return on their money invested to compensate for the various riskd they undertake like risks of maturity, interest rate, default, liquidity and inflation.

So the value of $1 today is less than $1 after one year . The money needs to multiply in value to avoid devaluation. The multiplication of money in value due to compounding effect is called the time value of money.

                 1 Future Value of Annuity =FV= A*[(1+k)^n-1]/k n=32 years k= 10% pa A= yearly $5000 FV =5000*(1.10^32-1)/0.10 FV =1005689 So the FV of the nest is $ 1,005,689                  2 When start at 34 Future Value of Annuity =FV= A*[(1+k)^n-1]/k n=22 years k= 10% pa A= yearly $5000 FV =5000*(1.10^22-1)/0.10 Future value =$357,014                  3 WHEN START SAVING AT 44 Future Value of Annuity =FV= A*[(1+k)^n-1]/k n=12 years k= 10% pa A= yearly $5000 FV =5000*(1.10^12-1)/0.10 Future value =$106,921 (Approx $107,000) Second Example Future Value of Annuity =FV= A*[(1+k)^n-1]/k n=10 years k= 10% pa A= yearly $2000 FV =2000*(1.10^10-1)/0.10 FV of the $2000 annuity will be $31875 at the age of 35 Karen adds $20,000. to the fund at age 35 So value of fund $51,875 It is further invested for 30 years @10% Maturity value =51875*1.1^30= $           905,188 So the maturity value woulkd be $905,188 not $556,000 So all the examples hold true except the last one

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