Question
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 first need to calculate how much interest each option will earn over the 3-year period.
Option 1: Simple interest
Interest earned = principal x rate x time
= $7,000 x 0.15 x 3
= $3,150
Option 2: Compound interest
We need to use the formula for compound interest to calculate the final amount after 3 years.
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal (initial investment)
r = interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, P = $7,000, r = 0.12, n = 4 (quarterly compounding), and t = 3.
A = $7,000(1 + 0.12/4)^(4*3)
= $7,000(1 + 0.03)^12
= $7,000(1.03)^12
= $7,000(1.4257)
= $9,879.90
Interest earned = final amount - principal
= $9,879.90 - $7,000
= $2,879.90
Therefore, the difference in interest earnings between the two options is:
$3,150 - $2,879.90 = $270.10
Option 1 (simple interest) will give Angel $270.10 more in financial returns compared to Option 2 (compound interest with quarterly compounding).