A man wants to make a $20,000 investment into a bank account towards college education for his grandchild. Assume this will be ready in 18 years. The man plans to pay 5% interest compounded monthly. Calculate the future value of this investment. Will this investment cover the average cost of college education today? What about the future?

Question

A man wants to make a $20,000 investment into a bank account towards college education for his grandchild. Assume this will be ready in 18 years.  The man plans to pay 5% interest compounded monthly. Calculate the future value of this investment.  Will this investment cover the average cost of college education today? What about the future?

anonymous · Answer

Look into a college 529 savings plan.  This will cover inflation and pre-calculate what your grandchild will recieve upon college entrance.  

feel free to email me more,

timothyplett@stfrancis.edu

anonymous · Answer

The word pay is confusing. The lump sum P of 20,000 will grow to some FA at some percentage for 18 years. Then it will be paid out as a monthly annuity for 48 months. Converting 5% monthly to an annual rate is difficult for th 20,000. 
As far as today is concerned, find the PV of 48 payments at 5% monthly for some tuition amount , say the tuition at a local college. Since tuition is paid twice per year over four years, this gets a little complicated. Try drawing time lines using the information in the attached file.

gw2011 · Answer

Assuming that the interest to be received is 5% per year but will be compounded monthly, the formula is:

FV=PV[1+(i/m)]^mn
where m=interest paid m times per year
where n=the number of years the interest is paid

FV=20,000[1+(0.05/12)]^(12)(18)
FV=20,000(1+0.0042)^(12)(18)
FV=20,000(1.0042)^216
FV=$49,453 approximately