Question

What is the formula for the compound amount of an investment compounded annually?

Answer 1

The compound amount of an investment compounded annually is calculated using the formula: Total Future Value = Principal × (1 + interest rate)^time. For example, a $3,000 principal at a 7% annual interest rate for 40 years would grow to $44,923.

Step-by-step explanation:

The formula for the compound amount of an investment compounded annually can be expressed as follows:

Total Future Value = Principal × (1 + interest rate)time

Where:

• Principal is the initial amount of money invested.
• Interest rate is the annual interest rate (expressed as a decimal).
• Time is the number of years the money is invested.

For instance, if you start with a $3,000 investment at a 7% annual rate over 40 years, the compound amount will be calculated as:

$3,000 × (1 + 0.07)40 = $44,923

This demonstrates the power of compound interest over time, and why it's important to start saving early in life. To find the compound interest earned after a certain period, subtract the principal from the calculated future value.

Answer 2

Answer: Compound interest is the interest calculated on the principal and the interest accumulated over the previous years. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next years. In Mathematics, compound interest is usually denoted by C.I.

Compound Interest = Amount – Principal

Step-by-step explanation:

`A=P (1+R/N)^T`

Where,

A = amount

P = principal

r = rate of interest

t = time (in years)

Alternatively, we can write the formula as given below:

CI = A – P