Compound Interest If 8000 is invested in an account for...

Compound Interest If $\$ 8000$ is invested in an account for which interest is compounded continuously, find the amount of the investment at the end of 12 years for the following interest rates. $$ \begin{array}{l}{\text { (a) } 2 \%} \\ {\text { (b) } 3 \%} \\ {\text { (c) } 4.5 \%} \\ {\text { (d) } 7 \%}\end{array} $$

Compound Interest If $\$ 8000$ is invested in an account for
which interest is compounded continuously, find the amount
of the investment at the end of 12 years for the following
interest rates.
$$
\begin{array}{l}{\text { (a) } 2 \%} \\ {\text { (b) } 3 \%} \\ {\text { (c) } 4.5 \%} \\ {\text { (d) } 7 \%}\end{array}
$$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Interest Rate

The interest rate is the proportion of the principal amount that is paid as interest over a set period. In compound interest calculations, the rate determines how quickly the investment grows, and varying the rate even slightly can lead to significantly different outcomes over an extended period.

Exponential Growth

Exponential growth describes a process where the quantity increases at a rate proportional to its current value; the classic example is money growing under compound interest. In the context of continuously compounded investment, the accumulation of interest grows exponentially over time, which dramatically increases the future value compared to linear growth.

Continuous Compounding

Continuous compounding is a mathematical limit where the frequency of compounding is increased infinitely, resulting in the formula A = Pe^(rt). This method uses the natural exponential function to determine the future value of an investment, given that interest is compounded at every possible moment.

Compound Interest

Compound interest is the process where the interest earned on an investment is reinvested to generate additional earnings over time. This means that the interest not only earns returns on the original principal but also on the accumulated interest from previous periods, leading to exponential growth over time.

Transcript

Please give Ace some feedback