It will cost $20,000 a year for four years to send an 8-year-old child to college. how much should be invested today if the child will make the first of four annual withdrawals 10 years from today? the expected rate of return is 8 percent.

To achieve their goal, they will need to invest $30,684.111 today

Explanation:

The value of money always reduces as time moves due to inflation. Therefor if we were to compare the current value of money now and maybe ten year ago, we notice that the value ten years ago was higher than the current value.  It was determined the amount of money used to buy a piece of property now was higher than the amount of money used to buy the same property ten years ago. In our case above, we need to determine the present value of the future cash flows that will be needed to be invested today in order to meet the child's college education. This can be achieved as follows using the formula below;

P.V=C/(1+r)^n

where;

P.V=present value=unknown

C=future cash flows=$20,000 per year

r=rate of return=8%=8/100=0.08

n=number of year

Year                                 Present Value                         Result

11                                   {20,000/(1+0.08)^11}                 8,577.657

12                                  {20,000/(1+0.08)^12}                7,943.275

13                                  {20,000/(1+0.08)^13}                7,353.958

14                                  {20,000/(1+0.08)^14}                6,809.221

Total=(8,577.657+7,943.275+7,353.958+6,809.221)=$30,684.111

To achieve their goal, they will need to invest $30,684.111 today

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