Question

An investment of $1000 was made for 3 years at 4% interest compounded annually. How much was the principal?

Answer 1

The original principal on a $1000 investment at 4% interest compounded annually for 3 years was approximately $888.996. Compound interest is calculated on both the initial principal and the accumulated interest, leading to potentially greater amounts than with simple interest.

Step-by-step explanation:

The student's question pertains to determining the original principal amount in a compound interest scenario, where an investment is made for a period of time with the interest being compounded annually. In this case, the investment amount is $1000 made for 3 years at a 4% annual interest rate.

To calculate the principal (P) after a certain number of years (t), at an annual interest rate (r), compounded annually, we use the formula:

P = A / (1 + r)^t

Where A is the amount of money accumulated after n years, including interest. Here, A is $1000, r is 0.04 (4% expressed as a decimal), and t is 3 years.

Now, let's calculate the principal:

P = $1000 / (1 + 0.04)^3

P = $1000 / (1.04)^3

P = $1000 / 1.124864

P ≈ $888.996

So, the original principal was approximately $888.996. Compound interest is powerful; it's calculated not just on the principal, but also on the accumulated interest from previous periods, which can lead to a significant difference in growth over time compared to simple interest. This concept is crucial in understanding the value and impact of compound interest on investments.

Answer 2

The principal amount invested was approximately $889.27.

Step-by-step explanation:

The question involves calculating the principal amount invested, given the future value and the interest rate using the formula for compound interest. The principal can be calculated by rearranging the compound interest formula:

Future Value = Principal × (1 + Rate)^{n}

Where Future Value is the amount of money obtained after n years, Principal is the initial amount invested, Rate is the annual interest rate, and n is the number of years the money is invested.

To find the principal, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the total amount, P is the principal, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, we have A = $1000, r = 4%, n = 1 (compounded annually), and t = 3 years. Plugging in these values, we get 1000 = P(1 + 0.04/1)^(1*3). Simplifying further, we get 1000 = P(1.04)^3. Dividing both sides by (1.04)^3, we find that the principal, P, is approximately $889.27.