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 investment option is best for her.(1 point)
Responses
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.
Aria should invest with 6.5% simple interest because it will result in $187.26 more in interest earnings.
Aria should invest with 6.5% simple interest because it will result in $26.69 more in interest earnings.
To calculate the simple interest, we multiply the principal amount ($6,700) by the interest rate (6.5%) and the number of years (3):
Simple Interest = $6,700 * 0.065 * 3 = $1,386.90
To calculate the compound interest, we use the formula:
Compound Interest = P(1 + r/n)^(nt) - P
Where:
P = Principal amount ($6,700)
r = annual interest rate as a decimal (6% or 0.06)
n = number of times interest is compounded per year (assume once per year)
t = number of years (3)
Compound Interest = $6,700(1 + 0.06/1)^(1*3) - $6,700 = $1,300.09
The difference between the two interest earnings is:
$1,386.90 - $1,300.09 = $86.81
Therefore, Aria should invest with 6.5% simple interest because it will result in $86.81 more in interest earnings.