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).
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.
3 answers
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).
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).
1 answer