Question

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)

Answer 1

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).