What would be the difference at the end of one year between the simple interest earned on a deposit of $450 at 4.5% and the compound interest earned on $450 at 4.5% compounded annually?
$22.50
$22.25
$0
$20.25
since there is a single period of interest, the amounts are the same.
To calculate the difference between the simple interest and the compound interest, we first need to calculate the simple interest and the compound interest separately.
Simple Interest:
The formula for calculating simple interest is: Interest = Principal x Rate x Time
Given:
Principal (P) = $450
Rate (R) = 4.5%
Time (T) = 1 year
Using the formula:
Interest = $450 x 0.045 x 1
Interest = $20.25
Compound Interest:
The formula for calculating compound interest is: A = P(1 + r/n)^(nt) - P
where:
A = Final Amount
P = Principal
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
Given:
Principal (P) = $450
Rate (R) = 4.5% (as a decimal, 0.045)
Time (T) = 1 year
Compounded Annually (n = 1)
Using the formula:
A = $450(1 + 0.045/1)^(1*1) - $450
A = $450(1 + 0.045) - $450
A = $450(1.045) - $450
A = $470.25 - $450
A = $20.25
Finally, we can find the difference between the simple interest and the compound interest:
Difference = Compound Interest - Simple Interest
Difference = $20.25 - $20.25
Difference = $0
Therefore, the difference at the end of one year between the simple interest earned on a deposit of $450 at 4.5% and the compound interest earned on $450 at 4.5% compounded annually is $0.
To find the difference in interest earned between simple interest and compound interest, you need to calculate the interest for each type of interest and then subtract one from the other.
First, let's calculate the simple interest earned on a deposit of $450 at an interest rate of 4.5%. The formula for simple interest is:
Simple Interest = (Principal × Rate × Time) / 100
Given:
Principal = $450
Rate = 4.5%
Time = 1 year
Substituting these values into the formula:
Simple Interest = (450 × 4.5 × 1) / 100 = $20.25
Next, let's calculate the compound interest earned on $450 at a rate of 4.5% compounded annually.
The formula for compound interest is:
Compound Interest = Principal × [(1 + Rate / 100) ^ Time - 1]
Given:
Principal = $450
Rate = 4.5%
Time = 1 year
Substituting these values into the formula:
Compound Interest = 450 × [(1 + 4.5 / 100) ^ 1 - 1] = $22.50
Now, subtract the simple interest from the compound interest to find the difference:
Difference = Compound Interest - Simple Interest
Difference = $22.50 - $20.25 = $2.25
Therefore, the correct answer is $2.25. None of the options provided match this answer, so it seems there might be an error in the answer choices.