SOLUTION: Your first child has just been born. You want to give her a million dollars when she retires at age 64. If you invest your money at 13% compounded quarterly, how much do you need t

Algebra ->  Trigonometry-basics -> SOLUTION: Your first child has just been born. You want to give her a million dollars when she retires at age 64. If you invest your money at 13% compounded quarterly, how much do you need t      Log On


   

Question 960657: Your first child has just been born. You want to give her a million dollars when she retires at age 64. If you invest your money at 13% compounded quarterly, how much do you need to invest today so your child will have a million dollars in 64 years?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
One million = +10%5E6+
The formula for compound interest is:
+A+=+P%2A%28+1+%2B+r%2Fn+%29%5E%28n%2At%29+
Principle is compounded quarterly, so
+n+=+4+
+A+=+10%5E6+
+t+=+64+
+r+=+.13+
-------------
+A+=+P%2A%28+1+%2B+r%2Fn+%29%5E%28n%2At%29+
+10%5E6+=+P%2A%28+1+%2B+.13%2F4+%29%5E%28+4%2A64+%29+
+10%5E6+=+P%2A1.0325%5E256++
+10%5E6+=+P%2A3596.2961+
+P+=+10%5E6+%2F+3596.2961+
+P+=+278.06+
You need to invest $278.06 today
check:
+10%5E6+=+P%2A%28+1+%2B+.13%2F4+%29%5E%28+4%2A64+%29+
+10%5E6+=+278.06%2A%28+1+%2B+.13%2F4+%29%5E%28+4%2A64+%29+
+10%5E6+=+278.06%2A1.0325%5E256+
Take the log of both sides
+6+=+log%28+278.06+%29+%2B+256%2Alog%28+1.0325+%29+
+6+=+2.4441+%2B+256%2A.01389+
+6+=+2.4441+%2B+3.5559+
+6+=+6+
OK