Compound Interest formula solution
P[1+r/100]t?
The expression P[1+r/100]^t represents the formula for compound interest. Here's how you can solve it step by step:
1. Start with the given values: P (the principal amount), r (the annual interest rate as a percentage), and t (the number of years).
2. Divide r by 100 to convert it from a percentage to a decimal: r/100.
3. Add 1 to the decimal interest rate: 1 + r/100.
4. Raise the result to the power of t: (1 + r/100)^t.
5. Multiply the principal amount (P) by the result from step 4 to find the compound interest.
For example, let's say you have $1,000 as the principal amount, an annual interest rate of 5%, and you want to calculate the compound interest after 3 years.
1. P = $1,000
2. r/100 = 5/100 = 0.05
3. 1 + r/100 = 1 + 0.05 = 1.05
4. (1 + r/100)^t = 1.05^3 = 1.158
5. Compound Interest = P * (1 + r/100)^t = 1,000 * 1.158 = $1,158 (rounded to the nearest dollar)
So, the compound interest after 3 years would be $1,158.