SOLUTION: How do I take the monthly payment formula for compound interest and solve for t? The formula I am referring to is: A=P(1+r/n)^(nt) + M((1+r/n)^(nt) -1)(n/r) Where A= Future

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: How do I take the monthly payment formula for compound interest and solve for t? The formula I am referring to is: A=P(1+r/n)^(nt) + M((1+r/n)^(nt) -1)(n/r) Where A= Future       Log On


   

Question 1145264: How do I take the monthly payment formula for compound interest and solve for t?
The formula I am referring to is:
A=P(1+r/n)^(nt) + M((1+r/n)^(nt) -1)(n/r)
Where A= Future Value of the investment
P = Principle or Present Value of the investment
r = interest rate
n = number of times per year interest is compounded
t = the number of years it will take for the investment to mature
M = the monthly payment or regular contribution to the investment account
Thank you!
MM
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(53937) About Me  (Show Source):
You can put this solution on YOUR website!
.
If I understand correctly, you are given the formula


    A = P%281%2Br%2Fn%29%5E%28nt%29 + M%28%281%2Br%2Fn%29%5E%28nt%29+-1%29%28n%2Fr%29


and you want to express the monthly payment  M  via all other variables.



It is very simple procedure.


First, move the first term from the right side to the left side with the opposite sign;

then divide both sides by  %28%281%2Br%2Fn%29%5E%28nt%29+-1%29%28n%2Fr%29  to expess M 


    M = %28A+-+P%281%2Br%2Fn%29%5E%28nt%29%29%2F%28%281%2Br%2Fn%29%5E%28nt%29+-1%29%28n%2Fr%29%29


Solved, explained and completed.



Answer by MathTherapy(10858) About Me  (Show Source):
You can put this solution on YOUR website!
How do I take the monthly payment formula for compound interest and solve for t?
The formula I am referring to is:
A=P(1+r/n)^(nt) + M((1+r/n)^(nt) -1)(n/r)
Where A= Future Value of the investment
P = Principle or Present Value of the investment
r = interest rate
n = number of times per year interest is compounded
t = the number of years it will take for the investment to mature
M = the monthly payment or regular contribution to the investment account
Thank you!
MM
In order to solve for t, we need to get that variable by ITSELF



 ------- Multiplying last 2 expressions

 --------- Distributing last expression

 --------- Adding Mn%2Fr to both sides

 ------------------ Factoring out right side

 ---------------- Dividing both sides by P+%2B+%28Mn%2Fr%29



 ---------- Applying KCF to left side

 ----------------------- Cancelling and simplifying left-side fractions

 ------------------ Converting to LOGS



That's it! Quite GRUELING, I might add!!