# Mr. and Mrs. Castro want to prepare for their 12 year old son's college education. If they invest 4000000 now at 8% compounded semi annually and they need 5000000 when he is 16 yrs old, will they...

Mr. and Mrs. Castro want to prepare for their 12 year old son's college education. If they invest 4000000 now at 8% compounded semi annually and they need 5000000 when he is 16 yrs old, will they have enough money by then?

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Mr. and Mrs. Castro want to prepare for their 12 year old son's college education and require $5,000,000 when he is 16.

If 4,000,000 is invested now at 8% compounded semi-annually after 4 years it will increase to:

`4000000*(1+0.04)^8 = 5474276.2`

**The Castros will have enough for their son's college with the amount invested.**

Age of the son now = 12 year

Age of the son when he goes to college = 16 years

Time available to prepare = 16-12 = 4 years

Amount invested = x = 4,000,000

Rate of interest = r = 8%

Investment Period = t = 4 years

Amount after 4 years = x(1+r)^t

= 4000000*(1+0.8)^4

= 5,441,956

The amount required for college education is 5,000,000 whereas the investment of 4,000,000 after four years will be 5,441,956 so:

* Mr. and Mrs. Castro will have enough money for college *by the time their son is 16 years.