Parents want to invest a sum of money at the birth of a child so that when the child becomes 18 years of age, the child will receive $20,000 per year toward college expenses in four yearly installments. If the nominal rate of return per year is 6%, and interest is compounded semi-annually, how much should the original investment be? 2. First, find the effective annual rate of return.$\displaystyle 1+i = \left( 1+\frac{0.06}{2} \right)^2\displaystyle i=6.09\%$Now, find the value of 4 payments of 20000, paid in advance$\displaystyle v=\frac{1}{1+i}\displaystyle d=iv\displaystyle PV = 20000 \times \frac{1-v^4}{d}\displaystyle PV = 20000 \times 3.66857\displaystyle PV = 73371.34$Now, these payments start on the 18th birthday. their value at birth is$\displaystyle PV' = 73371.34 \times v^{18}\displaystyle PV' = 25315.49\$