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.
To find the difference in interest earnings, we need to calculate the interest earned with each investing option.
Option 1: Simple Interest
The formula for calculating simple interest is: I = P * r * t
where I is the interest earned, P is the principal amount (initial investment), r is the interest rate, and t is the time period.
Using the information given:
P = $7,000
r = 15% = 0.15
t = 3 years
I1 = 7,000 * 0.15 * 3 = $3,150
Option 2: Compound Interest
The formula for calculating compound interest with quarterly compounding is: A = P * (1 + r/n)^(n*t)
where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times compounding occurs per year, and t is the time period.
Using the information given:
P = $7,000
r = 12% = 0.12
n = 4 (quarterly compounding)
t = 3 years
A2 = 7,000 * (1+0.12/4)^(4*3) = $9,368.87
The interest earned in option 2 is the difference between the final amount and the principal amount:
I2 = A2 - P = 9,368.87 - 7,000 = $2,368.87
Therefore, the difference in interest earnings between the two options is:
Difference = I2 - I1 = 2,368.87 - 3,150 = -$781.13
The negative sign indicates that option 1 (investing with a 15% simple interest rate) will give more financial returns than option 2 (investing with a 12% compound interest rate, with interest compounded quarterly).
Try again
Apologies for the incorrect response earlier. Let's calculate the interest earned for each option correctly.
Option 1: Simple Interest
The formula for calculating simple interest is: I = P * r * t
Using the information given:
P = $7,000
r = 15% = 0.15
t = 3 years
I1 = 7,000 * 0.15 * 3 = $3,150
Option 2: Compound Interest
The formula for calculating compound interest is: A = P * (1 + r/n)^(n*t)
Using the information given:
P = $7,000
r = 12% = 0.12
n = 4 (quarterly compounding)
t = 3 years
A2 = 7,000 * (1 + 0.12/4)^(4*3) = $9,579.73
The interest earned in option 2 is the difference between the final amount and the principal amount:
I2 = A2 - P = 9,579.73 - 7,000 = $2,579.73
Therefore, the difference in interest earnings between the two options is:
Difference = I2 - I1 = 2,579.73 - 3,150 = -$570.27
The negative sign indicates that option 1 (investing with a 15% simple interest rate) will give more financial returns than option 2 (investing with a 12% compound interest rate, with interest compounded quarterly).