Asher cashed in a one-year term deposit after only five months had elapsed. In order to do so, he accepted an interest rate penalty—a reduction from the scheduled 5.5% rate of simple interest. If he was paid $145.83 interest on the $10,000 term deposit, what reduction was made in the per annum rate of simple interest?
I = PRT
145.83 = 10,000 * R * 0.4167
148.83 = 4,166.67R
148.83/4,166.67 = R
0.0357 = R
3.57% = R
Well, it seems like Asher couldn't wait to get his hands on his money! In his haste, he cashed in his term deposit after only five months. Poor guy, couldn't resist the temptation! Now, the interest he received was $145.83 on a $10,000 term deposit.
Let's see how much interest he would have received if he waited for the full year.
If the interest rate was 5.5% per annum, he would have received interest of:
(5.5/100) * $10,000 = $550
But instead, he received $145.83. So, the reduction in the interest rate penalty is:
$550 - $145.83 = $404.17
So, the reduction made in the per annum rate of simple interest was a whopping $404.17. Asher definitely learned that patience pays off!
To find the reduction in the per annum rate of simple interest, we first need to calculate the interest earned for the full one-year term deposit.
Given:
Principal (P) = $10,000
Interest earned (I) = $145.83
The formula for simple interest is:
I = P * r * t
Where:
I = Interest earned
P = Principal amount
r = Rate of interest
t = Time in years
We are given that the scheduled rate of interest is 5.5%, which is equivalent to 0.055 in decimal form.
To find the interest earned for the full one-year term, we can rearrange the formula:
I = P * r * t
Rearranging the formula to solve for the rate of interest (r):
r = I / (P * t)
Substituting the given values:
r = $145.83 / ($10,000 * 1)
Simplifying:
r = $145.83 / $10,000
r ≈ 0.014583
To find the reduction in the per annum rate of simple interest, we need to calculate the difference between the scheduled rate (5.5%) and the actual rate (0.014583):
Reduction = 5.5% - 0.014583
Reduction ≈ 5.485417%
Therefore, the reduction made in the per annum rate of simple interest is approximately 5.485417%.
To find the reduction in the per annum rate of simple interest, we need to determine the interest that would have been earned if the deposit had been held for the full year at the scheduled rate of 5.5%.
The formula for calculating simple interest is:
Interest = Principal x Rate x Time
Given:
Principal (P) = $10,000
Rate (R) = 5.5% (per annum)
Time (T) = 5 months (which is 5/12 of a year)
We can plug these values into the formula to find the interest earned at the scheduled rate:
Interest = $10,000 x 0.055 x (5/12)
Interest = $229.17
However, Asher cashed in the term deposit early and received only $145.83 in interest. This means he accepted a penalty, resulting in a reduction in the interest earned.
To find the reduction, we subtract the actual interest received from the interest that would have been earned:
Reduction = $229.17 - $145.83
Reduction = $83.34
Therefore, the reduction made in the per annum rate of simple interest is $83.34.