Aaron invested $7,500 in an account paying an interest rate of 1.5% compounded continuously. Assuming no deposits or withdrawals are made, how much money, *to the nearest hundred dollars*, would be in the account after 8 years?

To calculate the amount of money in the account after 8 years with continuous compounding, we use the formula for continuously compounded interest:

\[
A = P \times e^{rt}
\]

Where:
- $ A $ is the amount of money in the account after time $ t $.
- $ P $ is the principal amount (initial investment), which is $7,500.
- $ r $ is the annual interest rate (as a decimal), which is 1.5%, or 0.015.
- $ t $ is the time in years, which is 8 years.
- $ e $ is the base of the natural logarithm (approximately 2.71828).

Substituting the values:

\[
A = 7500 \times e^{(0.015 \times 8)}
\]

Let's calculate this.After 8 years, the amount of money in the account would be approximately **$8,500**, rounded to the nearest hundred dollars.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How much would the account hold after 10 years with the same interest rate?
2. What would the future value be if the interest rate were 2% instead of 1.5%?
3. How much interest would Aaron earn over 8 years?
4. How would the final amount change if the interest were compounded annually instead of continuously?
5. What is the effective annual rate (EAR) for the continuous compounding at 1.5%?

**Tip:** Continuous compounding grows money faster than periodic compounding because interest is added an infinite number of times per year, albeit in infinitesimally small amounts.

Discover how to calculate continuous compounding interest with an initial investment of $7,500, an interest rate of 1.5%, compounded continuously for 8 years. Learn the formula and steps to find the future value of investments with continuous compounding.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation