Martin takes out a simple-interest loan at 7.5 %. After 6 months, the amount of interest on the loan is $69.64. What was the amount of the loan?
is $522.30 correct
Interest amount I over a principal P at r% per annum for n years is:
I=Prn
69.64=P*0.075*0.5
Note: 0.075=7.5%, 0.5year=6 months.
solve for P to get
P=69.64/(0.075*0.5)=1857.07
Check:
Interest = 1857.07*0.075*0.5
=$69.64 OK.
=
To find the amount of the loan, we can use the formula for simple interest:
Interest = (Principal) x (Interest Rate) x (Time)
Let's denote the amount of the loan as "P". The interest rate is given as 7.5% or 0.075 in decimal form. The time is 6 months or 0.5 years.
We are given that the interest on the loan is $69.64. Plugging in these values into the formula, we can set up the equation:
69.64 = P x 0.075 x 0.5
To solve for P, we divide both sides of the equation by (0.075 x 0.5):
P = 69.64 / (0.075 x 0.5)
Simplifying the expression on the right-hand side:
P ≈ 928.53
Therefore, the amount of the loan is approximately $928.53, not $522.30.