POWER
Returns a number raised to a power.
Syntax:
POWER(number, power)
returns , that is number raised to the power of power. The same result may be achieved by using the exponentiation operator ^: number^power
Example:
POWER(4, 3)
returns 64, which is 4 to the power of 3.
4^3
also returns 4 to the power of 3.
Application:
The POWER function is often used in finance and engineering to calculate values that grow exponentially. A great application of this is calculating compound interest.
Let's imagine you are an investor looking to see how much your initial investment will be worth after a certain number of years.
Scenario:
You invest $1,000 in a savings account with a fixed annual interest rate of 5%. You want to calculate the final value of your investment after 1, 2, 3, 4, and 5 years.
The Formula:
The formula for compound interest is:
Where:
- A = the future value of the investment/loan, including interest
- P = the principal investment amount (the initial amount)
- r = the annual interest rate (as a decimal)
- t = the number of years the money is invested or borrowed for
The (1 + r)^t part of the formula can be easily calculated using the POWER function.
The syntax for the POWER function is: POWER(base, exponent)
In our example:
- base = (1+r)
- exponent = t
Our Values:
- P=1000
- r=0.05 (5% as a decimal)
The Table:
Here is a table showing the calculation for each year.
Year (t) | Principal (P) | Rate (r) | Base (1+r) | Exponent (t) | POWER(1.05, t) | Future Value (A) = 1000 * POWER(1.05, t) | ||
|---|---|---|---|---|---|---|---|---|
A | B | C | D | E | F | G | ||
1 | 1 | $1,000.00 | 0.05 | 1.05 | 1 | 1.05 | $1,050.00 | |
2 | 2 | $1,000.00 | 0.05 | 1.05 | 2 | 1.1025 | $1,102.50 | |
3 | 3 | $1,000.00 | 0.05 | 1.05 | 3 | 1.157625 | $1,157.63 | |
4 | 4 | $1,000.00 | 0.05 | 1.05 | 4 | 1.21550625 | $1,215.51 | |
5 | 5 | $1,000.00 | 0.05 | 1.05 | 5 | 1.276281563 | $1,276.28 |
As you can see, the POWER function simplifies the calculation by raising the base (1.05) to the power of the year (t), which represents the number of compounding periods. This is a fundamental operation in financial modeling to project the growth of investments over time.
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