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.
The difference in interest earnings is $ ___ and option ___ is the better investing option.
To find the difference in interest earnings, we need to calculate the interest earned for each option.
For Option 1:
Interest = Principal * Rate * Time
Interest = $7,000 * 0.15 * 3
Interest = $3,150
For Option 2:
Since interest is compounded quarterly, we need to calculate the compound interest using the formula:
A = P(1 + r/n)^(nt)
where:
A = final amount
P = principal amount
r = annual interest rate (as a decimal)
n = number of compounding periods per year
t = number of years
In this case, the annual interest rate is 12%, which is equivalent to 0.12 as a decimal. The interest is compounded quarterly, which means n = 4.
A = $7,000(1 + 0.12/4)^(4*3)
A = $7,000(1.03)^12
A ≈ $7,000(1.425)
Interest = A - P
Interest ≈ $9,975 - $7,000
Interest ≈ $2,975
The difference in interest earnings is $2,975 - $3,150 = -$175. Option 1 has a higher interest earnings.
Therefore, Option 1 is the better investing option.