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 for each option.
Option 1: Simple Interest
The formula to calculate simple interest is: I = P * r * t, where I is the interest, P is the principal amount, r is the interest rate, and t is the time in years.
For Option 1:
Principal = $7,000
Interest rate = 15% = 0.15
Time = 3 years
I1 = 7000 * 0.15 * 3
I1 = $3,150
Option 2: Compound Interest
The formula to calculate compound interest 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 the interest is compounded per year, and t is the time in years.
For Option 2:
Principal = $7,000
Interest rate = 12% = 0.12
Compounded quarterly, so n = 4 (4 times per year)
Time = 3 years
A2 = 7000 * (1 + 0.12/4)^(4*3)
A2 = $9,682.22
The interest earned for Option 2 is the final amount minus the principal amount: I2 = A2 - P
I2 = 9682.22 - 7000
I2 = $2,682.22
The difference in interest earnings is:
Difference = I2 - I1
Difference = 2682.22 - 3150
Difference = -$467.78
The difference in interest earnings between the two options is -$467.78. This means that Option 1 (investing with a 15% simple interest rate) will give Angel more financial returns compared to Option 2 (investing with a 12% compound interest rate with interest being compounded quarterly).
the difference is wrong
Apologies for the previous mistake. Let's recalculate the difference in interest earnings correctly.
Option 1: Simple Interest
Principal = $7,000
Interest rate = 15% = 0.15
Time = 3 years
I1 = 7000 * 0.15 * 3
I1 = $3,150
Option 2: Compound Interest
Principal = $7,000
Interest rate = 12% = 0.12
Compounded quarterly, so n = 4 (4 times per year)
Time = 3 years
A2 = 7000 * (1 + 0.12/4)^(4*3)
A2 = $8,424.15
The interest earned for Option 2 is the final amount minus the principal amount: I2 = A2 - P
I2 = 8424.15 - 7000
I2 = $1,424.15
The difference in interest earnings is:
Difference = I2 - I1
Difference = 1424.15 - 3150
Difference = -$1,725.85
The corrected difference in interest earnings between the two options is -$1,725.85. This means that Option 1 (investing with a 15% simple interest rate) will give Angel more financial returns compared to Option 2 (investing with a 12% compound interest rate with interest being compounded quarterly).