Question 335165: For a certain credit card, given a starting balance of P and an ending balance of A, the function below gives the number of months that have passed, assuming that there were no payments or additional purchases during that time. You started with a debt of $1000 and now owe $1210.26. For how many months has the debt been building? Use a calculator.
FORMULA: N=log A-log P/log (1.0175)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Starting balance is P which is equal to 1000.
Ending balance is A which is equal to 1210.26.
interest rate is equal to .075
formula for future value of a present amount is equal to:
A = P * (1.075)^n
A is the future amount.
P is the present value
1.075 is the interest rate of .075 + 1.
Divide both sides of this equation by P to get:
A/P = 1.075^n
Take the log of both sides of this equation to get:
log(A/P) = log(1.075^n).
Based on the laws of logarithms, this becomes:
log(A) - log(P) = n * log(1.075)
Divide both sides of this equation by log(1.075) to get:
n = ((log(A) - log(P)) / log (1.075)
Since A = 1210.26 and P = 1000, this equation becomes:
n = (log(1210.26) - log(1000)) / log(1.075)
Solve for logs of each of these numbers to get:
n = (3.08287868 - 3) / .031408464 which becomes:
n = .08287868 / .031408464 which becomes:
n = 2.638737097
If this is true, then it should satisfy the equation:
A = P * (1.075)^n
Substitute in this equation to get:
1210.26 = 1000 * (1.075)^2.638737097
Solve this equation using your calculator to get:
1210.26 = 1000 * 1.21026 = 1210.26 which is true, confirming the value for n is good.
|
|
|
