$177,000 is invested at 4.5% per annum for 8 years. Find the amount the investment is worth at the end if it is compounded monthly.

To solve this problem, we'll use the formula for compound interest:

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

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

Given:
- $ P = 177,000 $ dollars
- $ r = 4.5\% = 0.045 $ (as a decimal)
- $ n = 12 $ (since the interest is compounded monthly)
- $ t = 8 $ years

Now, substitute the values into the formula:

\[
A = 177,000 \left(1 + \frac{0.045}{12}\right)^{12 \times 8}
\]

Let's calculate this step by step.

1. Calculate $ \frac{r}{n} = \frac{0.045}{12} $.
2. Add 1 to the result.
3. Raise the result to the power of $ 12 \times 8 = 96 $.
4. Multiply by the principal $ P = 177,000 $.

Let's compute that.The investment will be worth approximately **$253,528.54** at the end of 8 years when compounded monthly at an annual interest rate of 4.5%.

Would you like more details, or do you have any questions?

Here are 5 related questions to consider:
1. What would the amount be if the interest was compounded annually instead of monthly?
2. How much interest is earned on the investment over the 8 years?
3. What is the formula for continuous compounding, and how would the result differ using that method?
4. How would the final amount change if the interest rate was 5% instead of 4.5%?
5. What if the investment period was extended to 10 years instead of 8 years?

**Tip:** When dealing with compound interest, the more frequently the interest is compounded, the greater the final amount will be.

Discover how to calculate the future value of a $177,000 investment at a 4.5% annual interest rate compounded monthly over 8 years. This detailed solution explains the compound interest formula and the impact of monthly compounding, perfect 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