An investment earning simple interest at a rate of 1.10% per annum for a term of 5 years earned $82.50 in interest. What was the principal?
I = PRT
82.5 = P * 0.011 * 5
82.5 = 0.055P
1,500 = P
To find the principal, we need to use the formula for calculating simple interest:
Simple Interest = Principal x Rate x Time
We are given that the rate is 1.10% per annum, which can be written as 0.011 in decimal form. The time is 5 years, and the interest earned is $82.50. Let's plug in these values into the formula:
82.50 = Principal x 0.011 x 5
To isolate the Principal, we divide both sides of the equation by (0.011 x 5):
82.50 / (0.011 x 5) = Principal
Simplifying the right side of the equation:
82.50 / 0.55 = Principal
Principal ≈ $150
To find the principal, we can use the formula for simple interest:
Simple Interest = (Principal * Rate * Time)
We are given the following information:
Simple Interest = $82.50
Rate = 1.10% per annum
Time = 5 years
Let's substitute these values into the formula and solve for the principal:
$82.50 = (Principal * 1.10% * 5)
To solve for the principal, we need to convert the interest rate from a percentage to a decimal:
1.10% = 0.011
Substituting this into the equation, we have:
$82.50 = (Principal * 0.011 * 5)
Now, we can solve for the principal by dividing both sides of the equation by (0.011 * 5):
$82.50 / (0.011 * 5) = Principal
Calculating this expression, we find:
$82.50 / 0.055 = Principal
Principal ≈ $1,500
Therefore, the principal amount was approximately $1,500.