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.
To find the difference in interest earnings, we can calculate the interest earned for each option and then subtract the interest earned from option 1 from the interest earned from option 2.
Option 1:
Simple interest formula: I = P * r * t
Where:
I = interest earned
P = principal amount (initial investment)
r = interest rate
t = time in years
I1 = 7000 * 0.15 * 3
I1 = $3,150
Option 2:
Compound interest formula: A = P * (1 + r/n)^(n*t)
Where:
A = ending balance (including interest)
P = principal amount (initial investment)
r = interest rate
n = number of times interest is compounded per year
t = time in years
A2 = 7000 * (1 + 0.12/4)^(4*3)
A2 = $9,356.69
Interest earned in option 2:
I2 = A2 - P
I2 = $9,356.69 - $7,000
I2 = $2,356.69
Difference in interest earnings:
Difference = I2 - I1
Difference = $2,356.69 - $3,150
Difference = -$793.31
The difference in interest earnings is -$793.31, which means that option 1 (15% simple interest) will give Angel more financial returns compared to option 2 (12% compound interest, compounded quarterly).