our goal is to create a college fund for your child. Suppose you find a fund that offers an APR of 6 %. How much should you deposit monthly to accumulate ​$83 comma 000 in 18 ​years?

You should invest ​$
  

To determine how much you should deposit monthly to accumulate $83,000 in 18 years with an APR (Annual Percentage Rate) of 6%, we will use the formula for the future value of a series of monthly deposits:

\[
FV = P \times \frac{(1 + r/n)^{nt} - 1}{r/n}
\]

Where:
- $ FV $ = Future Value (target amount, which is $83,000)
- $ P $ = Monthly deposit (what we are solving for)
- $ r $ = Annual interest rate (6% or 0.06)
- $ t $ = Time in years (18 years)
- $ n $ = Number of times the interest is compounded per year (since deposits are monthly, $ n = 12 $)

Rearranging the formula to solve for $ P $:

\[
P = \frac{FV \times r/n}{(1 + r/n)^{nt} - 1}
\]

Let me now calculate this.You should invest approximately **$214.27** per month to accumulate $83,000 in 18 years with a 6% annual interest rate.

Would you like more details on how this calculation was done or have any questions?

Here are 5 related questions to consider:
1. How does changing the interest rate affect the monthly deposit?
2. What if the savings period is shorter, say 10 years?
3. How much will you accumulate if you deposit a higher amount each month?
4. What happens if the interest compounds more frequently than monthly?
5. How does inflation impact the real value of $83,000 after 18 years?

**Tip:** Starting early with compound interest investments reduces the amount you need to save each month.

Our goal is to create a college fund for your child. Suppose you find a fund that offers an APR of 6%. How much should you deposit monthly to accumulate $83,000 in 18 years?

Find out how much you need to deposit monthly to accumulate $83,000 over 18 years with a 6% APR. This solution involves compound interest formulas and explains how future value and monthly deposits interact. Ideal for students learning financial math.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation