Suppose $1000 is invested for 10 years at 6% compounded annually. a. Find the compound amount. b. Find the compound interest.
Understand the Problem
The image shows an example of calculating compound amount and compound interest. The problem involves an investment of $1000 for 10 years at 6% compounded annually. Part (a) asks to find the compound amount, and part (b) asks to find the compound interest.
Answer
a. $S \approx $1790.85$ b. Compound Interest $= $790.85$
Answer for screen readers
a. The compound amount is approximately $1790.85. b. The compound interest is $790.85.
Steps to Solve
- Calculate the Compound Amount The formula for compound amount $S$ is given by $S = P(1 + r)^n $, where $P$ is the principal amount, $r$ is the interest rate, and $n$ is the number of compounding periods. In this case, $P = 1000$, $r = 0.06$, and $n = 10$. Substitute the values into the formula:
$S = 1000(1 + 0.06)^{10} = 1000(1.06)^{10}$ $S \approx 1000 \times 1.790847697 = 1790.847697$
Round the result to two decimal places since we are dealing with money. $S \approx 1790.85$
- Calculate the Compound Interest The compound interest is the difference between the compound amount and the principal amount. Compound Interest $= S - P$ Given $S = 1790.85$ and $P = 1000$,
Compound Interest $= 1790.85 - 1000 = 790.85$
a. The compound amount is approximately $1790.85. b. The compound interest is $790.85.
More Information
The power of compound interest is that you earn interest not only on your initial investment (principal), but also on the accumulated interest from previous periods. This leads to exponential growth over time.
Tips
A common mistake is forgetting to raise $(1 + r)$ to the power of $n$. Also, one might confuse compound interest with simple interest. Compound interest considers the accumulated interest of previous periods, while simple interest does not.
AI-generated content may contain errors. Please verify critical information
