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 interest earnings for each option, we can use the following formulas:
Option 1 (Simple Interest):
Interest = Principal * Rate * Time
Interest = $7,000 * 0.15 * 3
Interest = $3,150
Option 2 (Compound Interest):
The formula for compound interest is given by:
Compound Interest = Principal * (1 + rate/n)^(n*time) - Principal
Where:
Principal = $7,000
Rate = 0.12 (12%)
n = 4 (quarterly compounding)
time = 3 years
Now, let's calculate the compound interest for Option 2:
Compound Interest = $7,000 * (1 + 0.12/4)^(4*3) - $7,000
Compound Interest ≈ $7,000 * (1.03)^(12) - $7,000
Using a calculator:
Compound Interest ≈ $7,000 * 1.425802 - $7,000
Compound Interest ≈ $9,980.61 - $7,000
Compound Interest ≈ $2,980.61
The difference in interest earnings is the compound interest minus the simple interest:
Interest earnings difference = Compound Interest - Simple Interest
Interest earnings difference = $2,980.61 - $3,150
Interest earnings difference ≈ -$169.39
So, the difference in interest earnings is approximately -$169.39.
Since the difference is negative, it means that Option 1 (investing with a 15% simple interest rate) will give higher returns compared to Option 2 (investing with a 12% compound interest rate compounded quarterly).