Question 5.11: Saving for College You estimate that you will need about $80...
Saving for College
You estimate that you will need about $80,000 to send your child to college in eight years. You have about $35,000 now. If you can earn 20 percent per year, will you make it? At what rate will you just reach your goal?
If you can earn 20 percent, the future value of your $35,000 in eight years will be:
FV=$35,000\times 1.20^{8} = $35,000×4.2998=$150,493.59
So, you will make it easily. The minimum rate is the unknown r in the following:
FV= $35,000 \times (1+r)^{8} =$80,000
(1+r)^{8} = $80,000/35,000=2.2857
Therefore, the future value factor is 2.2857. Looking at the row in Table A.1 that corresponds to eight periods, we see that our future value factor is roughly halfway between the ones shown for 10 percent (2.1436) and 12 percent (2.4760), so you will just reach your goal if you earn approximately 11 percent. To get the exact answer, we could use a financial calculator or we could solve for r:
(1+r)^{8} = $80,000/35,000=2.2857
1+r=2.2857^{(1/8)} =2.2857^{.125} =1.1089
r=10.89%