If you deposit $5000 into an account for 4 years, How much MORE interest would you earn by compounding vs simple interest of 5.5%?
A. $100
B. $1100*
C. $1194
D. $94
To calculate the difference in interest earned by compounding vs simple interest, we need to calculate the interest earned using both methods and find the difference.
For simple interest, the formula to calculate the interest earned can be calculated using the formula:
Simple Interest = Principal * Rate * Time
Where:
Principal = $5000
Rate = 5.5% (or 0.055 as a decimal)
Time = 4 years
Simple Interest = $5000 * 0.055 * 4
Simple Interest = $1100
For compound interest, the formula to calculate the interest earned is:
Compound Interest = P*(1+r/n)^(n*t) - P
Where:
P = Principal = $5000
r = Annual interest rate = 5.5% (or 0.055 as a decimal)
n = Number of times interest is compounded per year (Assuming compounded annually, so n = 1)
t = Number of years = 4
Compound Interest = $5000 * (1 + 0.055/1)^(1*4) - $5000
Compound Interest = $5000 * (1 + 0.055)^(4) - $5000
Compound Interest = $5000 * (1.055)^4 - $5000
Compound Interest = $5000 * 1.2480322 - $5000
Compound Interest = $1240.161
To find the difference in interest earned:
Difference = Compound Interest - Simple Interest
Difference = $1240.161 - $1100
Difference = $140.161
Therefore, the correct answer is B. $1100. The difference in interest earned by compounding vs simple interest is $140.161, which is closest to $1100.
You did not read the question carefully.
simple: 5000(1 + .055*4)
compound: 5000(1 + .055)^4
now subtract the simple amount from the compound amount.