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# Time Value of Money Concepts

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Al Corbin is 25 years old today and he wishes to accumulate enough money over the next 35 years to provide for a 20 year retirement annuity of \$100,000 at the beginning of each year, starting with his 60th birthday. He can save \$2,000 at the end of each of the next 10 years and \$3,000 each year for the following 10 years. How much must he save each year at the end of years 21 through 35 to obtain his goal? Assume that the average rate of return over the entire period will be 10%.

#### Solution Preview

First we calculate Future value of \$2000 annuity at the end of 10th year @10% rate of return.
Periodic deposit=R=\$2000
Number of periods=n=10
Rate of return=i=10%
S=R*((1+i)^n-1)/i=2000*((1+10%)^10-1)/10%=\$31874.85

Let us calculate how much this amount will become on his 60th birthday.
(period =25 years, rate of return=10%)
FV1=31874.85*(1+10%)^25 =\$345354.62 --------(1)

Now we calculate Future ...

#### Solution Summary

Solution describes the formulas and methodology to find out the the periodic savings in the given period so as to meet the desired financial objective.

\$2.19