John borrowed $1,000 discounted at 10% for six months. How much did he receive when the loan was made?
I get $952.38 by using the formula below:
1000=P(1+.10/2)^(.5*2) - am I doing this right?
To calculate the amount John received when the loan was made, we need to use the formula for the present value of a discounted loan.
The formula you mentioned is partially correct, but there is a mistake in the calculation. Here's how to correctly calculate the amount John received:
Present value formula: PV = FV / (1 + r)^n
Where:
PV = Present Value (the amount John received when the loan was made)
FV = Future Value (the amount John has to repay)
r = Interest rate per compounding period
n = Number of compounding periods
In this case, the Future Value (FV) is the amount John borrowed, which is $1,000. The interest rate per compounding period (r) is 10% or 0.10, and the loan duration is six months or 0.5 years.
Using the formula, we can calculate the Present Value (PV):
PV = 1000 / (1 + 0.10)^0.5
PV = 1000 / (1.10)^0.5
PV ≈ $951.29
Therefore, John received approximately $951.29 when the loan was made.