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.
Would answers 169.67 and option 2 be correct?
To find the interest earnings for each option, we can use the simple interest formula:
Option 1:
Interest = Principal x Rate x Time
Interest = $7,000 x 15% x 3 years
Interest = $7,000 x 0.15 x 3
Interest = $3,150
Option 2:
To calculate compound interest, we use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (in this case, $7,000)
r = the annual interest rate in decimal form (in this case, 12% or 0.12)
n = the number of times that interest is compounded per year (in this case, quarterly, so 4 times)
t = the number of years the money is invested for (in this case, 3 years)
Using the given values, we can calculate the compound interest for Option 2:
A = $7,000(1 + 0.12/4)^(4*3)
A = $7,000(1.03)^12
A ≈ $7,000(1.425364)
A ≈ $9,977.55
To find the interest earned, we subtract the principal:
Interest = A - P
Interest = $9,977.55 - $7,000
Interest ≈ $2,977.55
The difference in interest earnings between the two options is $2,977.55 - $3,150 ≈ -$172.45. Therefore, Option 2 would yield lower financial returns compared to Option 1.