Kira wants to save money to open a tutoring center. She buys an annuity with a monthly payment of $36 that pays 3.1% interest, compounded monthly. Payments will be made at the end of each month. Find the total value of the annuity in 7 years.

To find the total value of the annuity after 7 years, we can use the future value of an ordinary annuity formula:

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

Where:
- $FV$ is the future value of the annuity.
- $P$ is the monthly payment.
- $r$ is the monthly interest rate.
- $n$ is the total number of payments.

Given:
- $P = 36$ dollars (monthly payment),
- Annual interest rate $= 3.1\%$, so the monthly interest rate $r = \frac{3.1\%}{12} = \frac{0.031}{12} \approx 0.0025833$,
- Number of years $= 7$, so the total number of payments $n = 7 \times 12 = 84$.

Now, substitute these values into the formula:

\[
FV = 36 \times \frac{(1 + 0.0025833)^{84} - 1}{0.0025833}
\]

Let's calculate the future value $FV$.The total value of the annuity after 7 years is approximately **$3,372.34**.

Do you want more details or have any questions? 

Here are 5 related questions:
1. How does increasing the monthly payment affect the future value of an annuity?
2. What would the future value be if the interest rate was higher?
3. How does the compounding frequency impact the total value of an investment?
4. What if Kira decided to invest for 10 years instead of 7?
5. How does an annuity differ from a lump-sum investment?

**Tip:** When investing in annuities, it's important to consider the compounding frequency as it significantly impacts the growth of your investment.

Learn how to calculate the total value of an annuity with monthly payments using the future value formula. Given an annuity with a monthly payment of $36, an annual interest rate of 3.1%, compounded monthly, and a duration of 7 years, find the future value after all payments. Approximate result: $3,372.34.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation