At the time of her​ grandson's birth, a grandmother deposits $ 4000 in an account that pays 2.5 % compounded monthly. What will be the value of the account at the​ child's twenty-first​ birthday, assuming that no other deposits or withdrawals are made during this​ period?

We are given an initial deposit (principal) of $4000, an interest rate of 2.5% compounded monthly, and a time period of 21 years. To find the future value of the account at the child's twenty-first birthday, we will use the formula for compound interest:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $A$ is the future value of the investment/loan, including interest
- $P$ is the principal amount (the initial deposit), which is $4000
- $r$ is the annual interest rate (decimal), so $r = 2.5\% = 0.025$
- $n$ is the number of times that interest is compounded per year, which is 12 for monthly compounding
- $t$ is the time the money is invested for, in years, which is 21 years.

Now let's calculate it step by step.

\[
A = 4000 \left(1 + \frac{0.025}{12}\right)^{12 \times 21}
\]

Let's solve for $A$.It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can still calculate the future value with the following formula:

\[
A = 4000 \left(1 + \frac{0.025}{12}\right)^{12 \times 21}
\]

The steps to calculate it:
1. Calculate $\frac{0.025}{12} = 0.0020833$
2. Raise $(1 + 0.0020833)$ to the power of $12 \times 21 = 252$
3. Multiply the result by 4000.

Would you like more details on how to handle similar problems?

Here are 5 related questions:
1. What happens if the interest is compounded quarterly instead of monthly?
2. How does the final value change if the interest rate increases to 3%?
3. What would be the future value after 25 years instead of 21 years?
4. How does continuous compounding differ from monthly compounding?
5. How much total interest is earned after 21 years?

**Tip:** The more frequently interest is compounded, the higher the future value will be!

At the time of her grandson's birth, a grandmother deposits $4000 in an account that pays 2.5% compounded monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period?

Calculate the future value of a $4000 deposit with 2.5% interest compounded monthly over 21 years. This example applies the compound interest formula, showing how interest grows over time. Perfect for students in Grades 10-12 studying financial mathematics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation