Matilda wishes to retire at age 67
 with $1,100,000
 in her retirement account. When she turns 28
, she decides to begin depositing money into an account with an APR of 9%
 compounded monthly. What is the monthly deposit that Matilda must make in order to reach her goal? Round your answer to the nearest cent, if necessary.



To determine the monthly deposit Matilda must make to reach her goal of $1,100,000 by age 67, we can use the formula for the future value of an ordinary annuity (which is the scenario where she makes regular monthly deposits into her retirement account):

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

Where:
- $FV$ is the future value (amount Matilda wants to have at retirement: \$1,100,000).
- $P$ is the monthly deposit (what we are solving for).
- $r$ is the monthly interest rate (annual interest rate divided by 12).
- $n$ is the total number of deposits (number of months from age 28 to 67).

### Step 1: Identify the known values
- Matilda's retirement goal: $FV = 1,100,000$.
- Annual interest rate: 9%, so the monthly interest rate $r = \frac{9\%}{12} = 0.0075$.
- Time until retirement: 67 years - 28 years = 39 years.
- Number of months until retirement: $n = 39 \times 12 = 468$ months.

### Step 2: Use the formula
We will now solve for the monthly deposit $P$:

\[
1,100,000 = P \times \frac{(1 + 0.0075)^{468} - 1}{0.0075}
\]

Now, let's compute the value of $P$.Matilda must make monthly deposits of approximately **$257.71** to reach her goal of $1,100,000 by age 67.

Would you like more details or have any questions? Here are some related questions to explore:

1. What would happen if the APR changed to 8% instead of 9%?
2. How would the required deposit change if Matilda started saving at age 30 instead of 28?
3. What if Matilda wanted to retire earlier, at age 60? How would that affect her monthly deposits?
4. What if the interest was compounded annually instead of monthly?
5. How much total interest would Matilda have earned by the time she retires?

**Tip:** Starting to invest earlier, even with a smaller amount, can significantly reduce the required contributions due to compound interest.

Matilda wishes to retire at age 67 with $1,100,000 in her retirement account. When she turns 28, she decides to begin depositing money into an account with an APR of 9% compounded monthly. What is the monthly deposit that Matilda must make in order to reach her goal? Round your answer to the nearest cent, if necessary.

Find out how much Matilda needs to deposit monthly to retire with $1,100,000 by age 67, given a 9% APR compounded monthly. This solution covers key financial math concepts like compound interest and annuities. Ideal for high school students studying finance and math concepts in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation