Question

A couple predicts that they will need to save $250,000 for their child's college education, and they predict that they will be able to earn about 9% interest, compounded monthly, on their investments. (a) If they begin the deposits at the end of each month when their child is a newborn, so that they have 18 years of deposits, how large must the deposit be? Round your final answer to two decimal places. 3. (b) If they do not begin making deposits until their child is 10 years old, so that they have only 8 years of deposits, how large must the deposit be? Round your final answer to two decimal places.

Answer 1

Let's use accumulation factor-compound formula:

`A=P(1+(r)/(n))^(nt)`

Where:

A = Future value or savings

P = Principal or initial investment

n = Number of times interest is compounded per year

t = time

(a) If they begin the deposits at the end of each month when their child is a newborn, so that they have 18 years of deposits, how large must the deposit be?

In this case:

A = 250000

P = ?

n = 12 (because the interest is compounded monthly)

t = 18

r=9% = 0.09

`\begin{gathered} 250000=P(1+(0.09)/(12))^(12\cdot18) \\ 250000=P(1.0075)^(216) \\ 250000=P(5.022637555) \\ \text{Solving for P:} \\ P=(250000)/(5.022637555)\approx49774.64 \end{gathered}`

If they do not begin making deposits until their child is 10 years old, so that they have only 8 years of deposits, how large must the deposit be? Round your final answer to two decimal places.​

In this case t changes from 18 to 8, therefore:

`\begin{gathered} 250000=P(1+(0.09)/(12))^(12\cdot8) \\ 250000=P(1.0075)^(96) \\ 250000=P(2.048921228) \\ \text{Solving for P:} \\ P=(250000)/(2.048921228)\approx122015.43 \end{gathered}`