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.
To find the difference between the two interest earning types, we first need to calculate the interest earned by each option.
For simple interest, we can use the formula:
Simple Interest = Principal * Rate * Time
In this case, the principal is $6,700, the rate is 6.5% (or 0.065 as a decimal), and the time is 3 years.
Simple Interest = $6,700 * 0.065 * 3 = $1,307.50
For compound interest, we can use the formula:
Compound Interest = Principal * (1 + Rate/100)^Time - Principal
In this case, the principal is again $6,700, the rate is 6% (or 0.06 as a decimal), and the time is 3 years.
Compound Interest = $6,700 * (1 + 0.06/100)^3 - $6,700
= $6,700 * (1.06)^3 - $6,700
= $6,700 * 1.191016 - $6,700
= $7,987.95 - $6,700
= $1,287.95
Now that we have calculated the interest earned by each option, we can find the difference:
Difference = Compound Interest - Simple Interest
= $1,287.95 - $1,307.50
= -$19.55
The difference between the two interest earning types is -$19.55. Hence, the compound interest option would earn $19.55 less in 3 years compared to the simple interest option.