Area is investing $6700 of her savings account for her summer job for her college fund. She is planning to invest the amount of 3 years. That can choose between simple interest at 6.5 and compounded. Interest at six find the difference between the two interest earning types to help area decide which investing option is best for her
To find the difference between the two interest earning types, we need to calculate the interest earned for each option and then subtract the simple interest from the compound interest.
1. Simple Interest:
The formula for simple interest is: I = P * r * t, where I is the interest earned, P is the principal (initial amount), r is the interest rate, and t is the time period in years.
For simple interest, the interest earned can be calculated as: I = 6700 * 0.065 * 3 = $1,317.
2. Compound Interest:
The formula for compound interest is: A = P * (1 + r/n)^(n*t), where A is the final amount, P is the principal, r is the interest rate, n is the number of times interest is compounded per year, and t is the time period in years.
Let's assume the interest is compounded annually (n = 1). The compound interest can be calculated as: A = 6700 * (1 + 0.065/1)^(1*3) = $7,897.447.
To calculate the compound interest earned, we subtract the principal amount: Compound interest = A - P = $7,897.447 - $6700 = $1197.447.
Now, we can find the difference between the compound interest and simple interest:
Difference = Compound interest - Simple interest = $1197.447 - $1,317 = -$119.553.
The difference between the compound interest and simple interest is -$119.553. This means that the simple interest option would earn $119.553 more than the compound interest option.