Questions: A man wants to set up a 529 college savings account for his granddaughter. How much would he need to deposit each year into the account in order to have 50,000 saved up for when she goes to college in 18 years, assuming the account earns a 6% return.

A man wants to set up a 529 college savings account for his granddaughter. How much would he need to deposit each year into the account in order to have 50,000 saved up for when she goes to college in 18 years, assuming the account earns a 6% return.

Transcript text: A man wants to set up a 529 college savings account for his granddaughter. How much would he need to deposit each year into the account in order to have $50,000 saved up for when she goes to college in 18 years, assuming the account earns a 6% return.

Solution

Solution Steps

Step 1: Understand the Problem

We need to determine the annual deposit \(D\) required to reach a saving goal \(S\) in \(n\) years, given an annual return rate \(r\).

Step 2: Apply the Formula

The formula to calculate \(D\) is derived from the future value of an annuity formula: \[D = S \times \frac{r}{(1 + r)^n - 1}\] Where:

\(S\) is the saving goal.
\(n\) is the number of years.
\(r\) is the annual return rate (in decimal).

Step 3: Substitute the Values and Calculate

Substituting \(S = 50000\), \(n = 18\), and \(r = 0.06\) into the formula, we get: \[D = 50000 \times \frac{0.06}{(1 + 0.06)^{18} - 1} = 1617.83\]

Final Answer:

The annual deposit needed to reach the saving goal of $50000 in 18 years, with an annual return rate of $6%$, is approximately $1617.83.

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