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% compounded interest rate, with interest being compounded quarterly
find the difference in interest earning to help angel determine which investing option will give more financial returns.
To find the difference in interest earnings between option 1 and option 2, we need to calculate the interest earned on each option separately.
Option 1: Simple Interest
The formula for simple interest is: Interest = Principal * Rate * Time
In this case, the principal is $7,000, the rate is 15% (or 0.15), and the time is 3 years.
Interest = $7,000 * 0.15 * 3 = $3,150
Option 2: Compounded Interest
To calculate compounded interest, we can use the formula: A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = principal amount
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years
In this case, the principal is $7,000, the rate is 12% (or 0.12), the interest is compounded quarterly (so n = 4), and the time is 3 years.
A = $7,000 * (1 + 0.12/4)^(4*3)
A = $7,000 * (1 + 0.03)^12
A ≈ $7,000 * (1.03)^12
A ≈ $7,000 * 1.425484139 $\approx$ $9,978.39
To find the interest earned on option 2, we need to subtract the principal amount ($7,000) from the future value ($9,978.39):
Interest = $9,978.39 - $7,000 = $2,978.39
Now, to find the difference in interest earnings, we subtract the interest earned in option 1 from the interest earned in option 2:
Difference in interest earnings = $2,978.39 - $3,150 ≈ -$171.61
Therefore, the difference in interest earnings between the two options is approximately -$171.61. This means that option 1 (investing with a 15% simple interest rate) would give more financial returns compared to option 2 (investing with a 12% compounded interest rate, with interest being compounded quarterly).