Find the simple interest on a $2,200 loan at 7% interest for 100 days. Use the
Banker’s rule, then compare to the amount of interest using a 365-day year
(a) i = Prt = 2200 * 0.07 * (100/360)
(b) ...
the answer
Well well well, you've got yourself a loan huh? Let's do some math and see how much interest you're gonna pay.
Using the Banker's rule, we're gonna calculate for 100 days, so that's like nearly a third of a year. The formula for simple interest is: Interest = Principal x Rate x Time
The principal amount is $2,200, the interest rate is 7%, and the time is 100 days. So let's plug those numbers in.
Interest = $2,200 x 0.07 x (100/365)
Now, calculate that and you'll find that the interest on your loan using the Banker's rule is approximately $42.60. But hey, let's not stop there!
Now, let's compare that to the amount of interest using a 365-day year. So, we're gonna pretend like the loan is for a whole year (365 days).
Interest using 365-day year = $2,200 x 0.07 x (365/365)
You know what the answer is gonna be? It's gonna be exactly $2,200 x 0.07, which is $154.
So, there you have it! According to the Banker's rule, you'll pay around $42.60 in interest for 100 days. But if we use a 365-day year, you're looking at paying $154.
It just goes to show you, the way interest is calculated can really make a difference!
To calculate the simple interest using the Banker's rule, we need to divide the interest rate by 360 and then multiply the result by the principal (loan amount) and the number of days.
Step 1: Convert the interest rate to a decimal:
7% = 7/100 = 0.07
Step 2: Calculate the simple interest using the Banker's rule:
Daily interest rate = 0.07 / 360 = 0.0001944
Interest = Daily interest rate * Principal * Number of days
Interest = 0.0001944 * $2,200 * 100 = $42.78
Now let's calculate the interest using a 365-day year:
Step 3: Convert the interest rate to a decimal:
7% = 7/100 = 0.07
Step 4: Calculate the simple interest using a 365-day year:
Daily interest rate = 0.07 / 365 = 0.0001918
Interest = Daily interest rate * Principal * Number of days
Interest = 0.0001918 * $2,200 * 100 = $41.82
Therefore, the simple interest on a $2,200 loan at 7% interest for 100 days using the Banker's rule is $42.78, while using a 365-day year it is $41.82.
To find the simple interest on a loan, we can use the formula: Interest = Principal x Rate x Time.
In this case, the Principal (amount of the loan) is $2,200 and the Rate is 7%.
First, let's calculate the interest using the Banker's rule (assuming 360 days in a year):
Interest = $2,200 x 7% x (100/360)
= $2,200 x 7% x 0.2778
= $43.5336
Therefore, the simple interest using the Banker's rule is approximately $43.53.
Next, let's calculate the interest using a 365-day year:
Interest = $2,200 x 7% x (100/365)
= $2,200 x 7% x 0.27397
= $44.9674
Therefore, the simple interest using a 365-day year is approximately $44.97.
To summarize,
Simple Interest using the Banker's rule = $43.53
Simple Interest using a 365-day year = $44.97
By comparing the two amounts, we can see that using the Banker's rule results in slightly lower interest compared to using the actual 365-day year method.