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).
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
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).
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).
1 answer