Solving for P in the formula to calculate principal that must be borrowed.

Question

Hey everyone!

So I have this problem that has to do with discount installment loans. The problem goes like this:

Suppose a loan has a face value of $1000, the interest rate is 15%, and the duration is 18 months. The interest is computed by multiplying the face value of $1000 by 0.15, to yield $150. That figure is then multiplied by the loan period 1.5 years (18 months) to yield $225 as the total interest owed. That amount is immediately deducted from the face value, leaving the consumer with only $775. Repayment is made in equal monthly installments based on the face value. So the monthly loan payment will be $1,000 divided by 18, which is $55.56. This calculation may not be too bad if the consumer needs $775 dollars, but the calculations get a bit more complicated if the consumer needs $1,000 dollars. Create a formula that can calculate the face value required in order for the consumer to recieve the $1000.

(Hint: Use this formula for calculating principal (P) that must be borrowed: net = P - (P * rate * time_in_years). Solve for P!!)

I am just really confused about how to create the formula that will solve this. Please help!!!

Answer 1

1000 = loan - loan fee

1000 = p - p(0.15)(1.8)