What is the principle and the interest?
A=$2719.50 P= ? r=6.1% t=20 years
What is the interest rate?
Balance= $3742.50 p=$3000 interest rate= ? t=45 months
Assuming simple Interest:
I = Po*r*t = 2719.50*0.061*20 = $3317.79
P = Po + I = 2719.50 + 3317.79=$6037.29.
P = Po + Po*r*t = $3742.50.
3000 + 3000*r*3.75 = 3742.50
3000 + 11250r = 3742.50
11250r = 3742.50-3000 = 742.50
r = 0.066 = 6.6%/yr.
To calculate the principle and the interest, you can use the following formulas:
1. Principle (P) = A - Interest
2. Interest = P * r * t
Now let's solve the first question.
1. Given: A=$2719.50, r=6.1%, t=20 years.
To find the principle, we'll use formula 1:
P = A - Interest
To find the interest, we'll use formula 2:
Interest = P * r * t
Inserting the known values into formula 2:
Interest = P * 0.061 * 20
Simplifying the formula:
Interest = 0.061 * 20P
Now, we can substitute this value for Interest in formula 1:
P = A - (0.061 * 20P)
Simplifying further:
P = A - 1.22P
Combining like terms:
2.22P = A
Substituting the given value for A (which is $2719.50):
2.22P = $2719.50
Dividing both sides by 2.22:
P = $2719.50 / 2.22
Calculating the value:
P ≈ $1225.68
Therefore, the principle (P) is approximately $1225.68.
Now let's solve the second question.
2. Given: Balance = $3742.50, P=$3000, t=45 months.
To find the interest rate, we'll rearrange formula 2 and solve for r:
Interest = P * r * t
Substituting the given values:
$3742.50 - $3000 = $3000 * r * (45/12)
Simplifying:
$742.50 = $3000 * r * 3.75
Dividing both sides by $3000 * 3.75:
r = $742.50 / ($3000 * 3.75)
Calculating the value:
r ≈ 0.066 or 6.6%
Therefore, the interest rate is approximately 6.6%.