solve for n in the formula A=p[i(1+i)^n/((1+i)^n)-1]

T

tegra97

New member
Joined
Sep 2, 2006
Messages
38
Im trying to figure out the interest rate (i) and number of payments (n) from the formula A=p[i(1+i)^n/((1+i)^n)-1] I'm having trouble solving for n and i someone please help? thanks.
 
this equation cannot be solved algebraically for (n) nor (i) ... each variable can only be solved for by numerical means.
 
Well I have numerical values for the variables (p,i,n,a) I just can't set up the equation to get i and n by itself. the first part says find the monthly interest rate which is i, and the second is finding how many months which is n.
 
perhaps you could provide the complete problem statement with the given numerical values?
 
If P is the total amount of money that is borrowed initially, the amount of the monthly payment,A can be determined from the formula A=P[(i(1+i)^n)/((1+i)^n)-1] where i is the monthly interest rate expressed as a fraction and n is the total number of payments. Suppose you borrow $10,000 to buy a car.
a)If you are required to repay $350 each month for 36 months, what is the corresponding monthly interest rate?
b) If you choose to repay $350 each month at the 0.006667 monthly interest rate, how many payments(months) will be required to repay the loan?

that's the problem. all i'm having trouble with is solving for n and i (setting up the equation, the steps on solving for n and i)
 
tegra97 said:
If P is the total amount of money that is borrowed initially, the amount of the monthly payment,A can be determined from the formula A=P[(i(1+i)^n)/((1+i)^n)-1] where i is the monthly interest rate expressed as a fraction and n is the total number of payments. Suppose you borrow $10,000 to buy a car.
a)If you are required to repay $350 each month for 36 months, what is the corresponding monthly interest rate?
b) If you choose to repay $350 each month at the 0.006667 monthly interest rate, how many payments(months) will be required to repay the loan?

that's the problem. all i'm having trouble with is solving for n and i (setting up the equation, the steps on solving for n and i)
Click to expand...

To start with, you're complicating the equation, plus using BAD variables;
change 'em to: A = Amount of money borrowed, P = monthly Payment:
doesn't that make more sense?

Formula is: P = Ai / [1 - 1/(1 + i)^n]
(yours will work, but is unnecessarily too wieldy)

As Mr Skeeter told you, that CANNOT be solved directly for i:
you need to use iteration; look that up using http://www.google.com

However, you CAN solve directly for n:

P = Ai / [1 - 1/(1 + i)^n]
Crisscross multiply:
Ai = P - P / (1 + i)^n
Simplify:
(1 + i)^n = P / (P - Ai)

n = log[P / (P - Ai)] / log(1 + i)

With your problem:
n = log[350 / (350 - 10000(.0066667))] / log(1 - .0066667) = ~31.8 months

By the way, that formula is usually "shown" in a still simpler manner:
P = Ai / (1 - v) where v = 1 / (1 + i)^n

Now, WHY teachers choose to show it in a form that requires 1 or 2 aspirins
to decipher, I'll never know :shock:
 
You must log in or register to reply here.
Top