Use the compound interest formula to compute the balance in the following account after the stated period of​ time, assuming interest is compounded annually.
​$37,000 invested at an APR of 4.7​% for 30 years.

To compute the balance in the account using the compound interest formula, we use the following formula:

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

Where:
- $ A $ is the amount of money accumulated after n years, including interest.
- $ P $ is the principal amount (initial investment).
- $ r $ is the annual interest rate (decimal).
- $ n $ is the number of times that interest is compounded per year.
- $ t $ is the time the money is invested for, in years.

For this problem:
- $ P = 37,000 $
- $ r = 4.7\% = 0.047 $
- $ n = 1 $ (compounded annually)
- $ t = 30 $ years

Plugging in the values:

\[
A = 37000 \left(1 + \frac{0.047}{1}\right)^{1 \times 30}
\]

Let's calculate the final amount.The balance in the account after 30 years, with an initial investment of $37,000 at an annual interest rate of 4.7% compounded annually, will be approximately **$146,758.13**.

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

1. How would the balance change if the interest were compounded semi-annually?
2. What would be the balance if the investment period were only 20 years?
3. How does changing the APR affect the final balance?
4. What is the difference between compounding annually and continuously?
5. How much total interest is earned over the 30 years?

**Tip:** The frequency of compounding can significantly affect the final amount. More frequent compounding periods lead to higher balances!

Use the compound interest formula to compute the balance in the following account after the stated period of​ time, assuming interest is compounded annually. $37,000 invested at an APR of 4.7​% for 30 years.

Learn how to calculate the balance of an account with an initial investment of $37,000 at a 4.7% annual interest rate compounded annually over 30 years. This guide covers the compound interest formula and provides a step-by-step solution. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation