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)
Option 1:
Simple interest is calculated using the formula: Interest = Principal x Rate x Time
Interest = 7000 x 0.15 x 3
Interest = 3150
Option 2:
Compound interest is calculated using the formula: A = P(1 + r/n)^(nt) - P
A = 7000(1 + 0.12/4)^(4*3) - 7000
A = 7000(1.03)^12 - 7000
A = 7659.03 - 7000
A = 659.03
The difference in interest earnings is: 659.03 - 3150 = -2490.97
Therefore, Option 1 will give more financial returns.
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)
To find the difference in interest earnings, we need to calculate the interest earned for each option and then find the difference between the two.
Option 1:
Interest = Principal x Rate x Time
Interest = $7,000 x 0.15 x 3
Interest = $3,150
Option 2:
Compound interest formula: A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal amount ($7,000)
r = annual interest rate (12% or 0.12)
n = number of times interest is compounded per year (quarterly or 4 times)
t = number of years (3 years)
A = $7,000(1 + 0.12/4)^(4*3)
A = $7,000(1.03)^12
A ≈ $9,456.98
Interest earned = final amount - principal amount
Interest = $9,456.98 - $7,000
Interest ≈ $2,456.98
Difference = Interest earned from Option 2 - Interest earned from Option 1
Difference = $2,456.98 - $3,150
Difference = -$693.02
Therefore, the difference in interest earnings is -$693.02. This means that Option 1 (investing with a 15% simple interest rate) will give more financial returns compared to Option 2 (investing with a 12% compound interest rate compounded quarterly).