A sum of $7260 is invested at 11 1/4 % simple interest for one year. The amount, in dollars, that must be invested at 7 1/2% simple interest for one year to earn the same amount of interest?
10890
7260 * (11.25/7.5)
To find the amount that must be invested at 7 1/2% simple interest to earn the same amount of interest as the $7260 invested at 11 1/4% interest, we need to calculate the interest earned on the initial investment and then determine the principal amount for the second investment.
First, let's calculate the interest earned on the initial investment at 11 1/4% interest for one year. We can use the simple interest formula:
Interest = (Principal * Rate * Time) / 100
In this case, the interest earned is equal to the principal amount invested ($7260) multiplied by the rate of interest (11 1/4%) and the time period (1 year), divided by 100:
Interest = (7260 * 11.25 * 1) / 100
Interest = 816.75
So, the interest earned on the initial investment is $816.75.
To find the principal amount for the second investment at 7 1/2% interest, we can rearrange the simple interest formula:
Principal = (Interest * 100) / (Rate * Time)
Substituting the values we have, the interest earned is $816.75, the rate of interest is 7 1/2% (or 7.5%), and the time period is 1 year:
Principal = (816.75 * 100) / (7.5 * 1)
Principal = 10910
Therefore, the amount that must be invested at 7 1/2% simple interest for one year to earn the same amount of interest as the $7260 invested at 11 1/4% interest is $10,910.
Well, well, well...looks like we have a math question in the house! Don't worry, I've got my clown calculator ready for action.
To find the amount that must be invested at 7 1/2% simple interest to earn the same amount of interest, we'll need to do some number crunching.
First, let's calculate the interest earned on the $7260 at 11 1/4% for one year:
Interest = Principal × Rate × Time
Interest = $7260 × 11.25% × 1 year
Okay, let me get my calculator. *Beep boop beep* Ah, here we go:
Interest = $7260 × 11.25% × 1 year
Interest = $817.50
Now that we know the interest earned, we can determine the amount needed to be invested at 7 1/2% simple interest to earn the same amount. Let's call it "X".
Interest = Principal × Rate × Time
$817.50 = X × 7.5% × 1 year
Time to whip out my clown calculator again. *Boopity boop beep*
$817.50 = X × 7.5% × 1 year
X = $817.50 ÷ (7.5% × 1 year)
Hold on to your funny bone...calculating... *Drum roll*
X = $817.50 ÷ (0.075 × 1 year)
X = $817.50 ÷ 0.075
X = $10,900
Ta-da! The amount that must be invested at 7 1/2% simple interest for one year to earn the same amount of interest is $10,900.
Now, you can go invest that money and start earning some clown-sized interest! 🎉