What is the formula for compound interest?

Steps to Solve

1. Identify the formula for compound interest The formula for calculating compound interest is given by: $$ A = P \left(1 + \frac{r}{100}\right)^t $$ where:

• $A$ is the amount of money accumulated after n years, including interest.
• $P$ is the principal amount (the initial amount of money).
• $r$ is the annual interest rate (in percentage).
• $t$ is the time the money is invested or borrowed for, in years.

2. Input the values into the formula For this problem:

• Principal, $P = 1500$
• Rate, $r = 5%$
• Time, $t = 3$ years

Plug the values into the formula: $$ A = 1500 \left(1 + \frac{5}{100}\right)^3 $$

3. Calculate the expression inside the parentheses Calculate $\frac{5}{100}$: $$ \frac{5}{100} = 0.05 $$ Then, the equation becomes: $$ A = 1500 \left(1 + 0.05\right)^3 = 1500 (1.05)^3 $$

4. Calculate $(1.05)^3$ Using the power: $$ (1.05)^3 = 1.157625 $$

5. Multiply by the principal Now, multiply by the principal: $$ A = 1500 \times 1.157625 = 1736.4375 $$

6. Calculate the compound interest The compound interest can be calculated using: $$ \text{Compound Interest} = A - P $$ So, $$ \text{Compound Interest} = 1736.4375 - 1500 = 236.4375 $$