A child’s grandparents wish to purchase a bond fund that matures in 18 years to be used for the grandchild’s college education. The bond fund pays 4% interest compounded semi-annually. How much should they purchase so that the bond fund will be worth 85,000 at maturity?

Solution

A c hi l d ’ s g r an d p a re n t s w i s h t o p u rc ha se a b o n d f u n d t ha t ma t u res in 18 ye a rs t o b e u se d f or t h e g r an d c hi l d ’ s co ll e g e e d u c a t i o n . T h e b o n d f u n d p a ys 4% in t eres t co m p o u n d e d se mi - ann u a ll y . Ho w m u c h s h o u l d t h ey p u rc ha se so t ha t t h e b o n d f u n d w i ll b e w or t h 85, 000 a t ma t u r i t y ?

Principal : 41668.97

Solution steps

Translate the problem into an equation:

85000 = P (1 + \frac{0.04}{2})^{2 \cdot 18}

Solve for

P, 85000 = P (1 + \frac{0.04}{2})^{2 \cdot 18} : P = 41668.97

Principal : 41668.97