Aria is investing $6,700 of her savings from her summer job for her college fund. She is planning to invest the amount for 3 years and can choose between simple interest at 6.5% and compound interest at 6%. Find the difference between the two interest earning types to help Aria decide which investing option is best for her.(1 point)
For the simple interest option, the interest earned would be calculated using the formula:
Interest = Principal * Rate * Time
Where:
Principal = $6,700
Rate = 6.5% = 0.065
Time = 3 years
Interest = 6700 * 0.065 * 3 = $1,301.50
For the compound interest option, the interest earned would be calculated using the formula:
Interest = Principal * (1 + Rate)^Time - Principal
Interest = 6700 * (1 + 0.06)^3 - 6700 = $1,313.70
The difference between the two interest earning types is:
Difference = Compound Interest - Simple Interest
Difference = $1,313.70 - $1,301.50 = $12.20
Therefore, the difference between the two interest earning types is $12.20.
these are the option ;
Aria should invest with 6.5% simple interest because it will result in $26.69 more in interest earnings.
Aria should invest with 6.5% simple interest because it will result in $187.26 more in interest earnings.
Aria should invest with 6% compound interest because it will result in $86.76 more in interest earnings.
Aria should invest with 6% compound interest because it will result in $73.81 more in interest earnings.
To find the correct option, we need to compare the interest earnings for both options.
For the simple interest option:
Interest = Principal * Rate * Time
Interest = 6700 * 0.065 * 3
Interest = $1,301.50
For the compound interest option:
Interest = Principal * (1 + Rate)^Time - Principal
Interest = 6700 * (1 + 0.06)^3 - 6700
Interest = $1,313.70
Now, let's compare the two options:
Option 1: Simple Interest at 6.5%
Interest = $1,301.50
Option 2: Compound Interest at 6%
Interest = $1,313.70
The correct statement is:
Aria should invest with 6% compound interest because it will result in $12.20 more in interest earnings.