Assume that you have $10,000 which you plan to invest for 3 years. How much more would you have if you invested the funds at 10% with annual compound interest versus 10% with simple interest? No funds will be paid until the end of the 3rd year.
Assume that you have $10,000 which you plan to invest for 3 years. How much more would you have if you invested the funds at 10% with annual compound interest versus 10% with simple interest? No funds will be paid until the end of the 3rd year.
To calculate the difference in returns between compound interest and simple interest, we need to understand the formulas for each type of interest.
1. Simple Interest:
Simple interest is calculated based on the initial principal amount (P), the interest rate (r), and the time period (t). The formula for calculating the interest is:
Simple Interest = P * r * t
In this case, the principal amount is $10,000, the interest rate is 10%, and the time period is 3 years. Plugging these values into the formula, we get:
Simple Interest = $10,000 * 0.10 * 3 = $3,000
Therefore, if the funds were invested with simple interest, you would have an additional $3,000 at the end of the 3rd year.
2. Compound Interest:
Compound interest is calculated by applying the interest rate to the initial principal amount and any accumulated interest. The formula for calculating compound interest is:
Compound Interest = P * (1 + r)^t - P
In this case, the principal amount is $10,000, the interest rate is 10%, and the time period is 3 years. Plugging these values into the formula, we get:
Compound Interest = $10,000 * (1 + 0.10)^3 - $10,000
Simplifying the equation:
Compound Interest = $10,000 * (1.10)^3 - $10,000
Compound Interest = $10,000 * 1.331 - $10,000
Compound Interest = $13,310 - $10,000
Compound Interest = $3,310
Therefore, if the funds were invested with compound interest, you would have an additional $3,310 at the end of the 3rd year.
To calculate the difference in returns, we subtract the simple interest from the compound interest:
Difference = Compound Interest - Simple Interest
Difference = $3,310 - $3,000
Difference = $310
Therefore, you would have an extra $310 if you invested the funds at a 10% annual compound interest rate compared to a 10% simple interest rate over 3 years.