How much should they deposit to reach their goal?

Question

Liz and Bob just had a baby named Isabelle, and they want to save enough money for Isabelle to go to college. Assume that they start making monthly payments when Isabelle is 5 into an ordinary annuity earning 7.04% and they calculate that they will need $30,200.00 by the time Isabelle turns 18 How much should they deposit every month so that they reach their goal?

Answer 1

Let be $S=30,200$ the sum they want to have at the 18th year, $i=\frac{7.04\%}{12}$ the effective monthly interest, $n=(18-5)\times 12=156$ the number of monthly instalments and $P$ the amount of the monthly installment. We have $$ S=P\times s_{\overline{n}|i}=P\times\frac{(1+i)^n-1}{i}\qquad\Longrightarrow\qquad P=\frac{S}{s_{\overline{n}|i}}=\frac{S}{\frac{(1+i)^n-1}{i}}=\frac{30,200}{254,08}=118,86 $$