Angel wants to invest $7,000 for 3 years. He has two investing options.
Option 1: Investing with a 15% simple interest rate.
Option 2: Investing with a 12% compound interest rate, with interest being compounded quarterly.
Find the difference in interest earnings to help Angel determine which investing option will give more financial returns.
(1 point)
The difference in interest earnings is $
, and option
is the better investing option.
To find the difference in interest earnings, we can calculate the amount of interest earned for each option.
For Option 1: Simple Interest
Interest = Principal * Rate * Time
Interest = $7,000 * 0.15 * 3 = $3,150
For Option 2: Compound Interest
Compound Interest Formula: A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount ($7,000)
r = the annual interest rate (0.12)
n = the number of times that interest is compounded per year (quarterly, so 4)
t = the number of years the money is invested for (3)
Using the formula:
A = $7,000(1 + 0.12/4)^(4*3) = $7,000(1 + 0.03)^12 = $7,000 * 1.03^12 ≈ $8,144.69
Interest earned = A - P = $8,144.69 - $7,000 = $1,144.69
Now, let's calculate the difference in interest earnings:
Difference in interest earnings = Compound interest - Simple interest
Difference in interest earnings = $1,144.69 - $3,150 = -$2,005.31
Since the difference in interest earnings is negative, it means that Option 1 (simple interest) earned more interest compared to Option 2 (compound interest).
Therefore, Option 1 is the better investing option.