Ann and tom want to establish a fund for their grandson's college education. what lump sum must they deposit at a 12.4% annual interest rate, compounded monthly, in order to have $30,000 in the fund at the end of 15 years?

A=P(1+r/n)^(tn)
n=number of times per year compounded
A=amount
P=principal inveseted
r=rate in decimal
t=time in years

so

we want A=30000
r=12.4%=0.124
t=15
monthyl means n=12

30000=P(1+0.124/12)^(15*12)
solve for P
easy, just divide both sides by (1.01033)^180
4714.97=P
that much must be invested