# Thread: Simple annual investment: express total accumulated amt as fcn of t

1. ## Simple annual investment: express total accumulated amt as fcn of t

If a principal of P dollars is invested at a simple annual interest rate of r for t years, express the total accumulated amount of the principal and interest as a function of t. Is your result a linear function of t?

-Would appreciate immediate help. I'm studying for a university test tomorrow.

2. Originally Posted by munclesonkey
If a principal of P dollars is invested at a simple annual interest rate of r for t years, express the total accumulated amount of the principal and interest as a function of t. Is your result a linear function of t?

-Would appreciate immediate help. I'm studying for a university test tomorrow.
What is the simple-interest formula? What equation then would represent the ending total amount?

When you solved this equation for "t=", what did you get?

3. Originally Posted by stapel
What is the simple-interest formula? What equation then would represent the ending total amount?

When you solved this equation for "t=", what did you get?

T=I/pr

4. A = accumulated amount

P = principal

r = decimal form of interest rate

t = elapsed time (in years)

The phrase "accumulated amount" means: principal plus interest.

In other words, if symbol I represents the interest, we have:

A = P + I

Now, replace symbol I with the math expression you were given for simple interest.

A will then be a function of t.

t and A(t) are the input and output variables, respectively.

P and r are constants (parameters).

5. Originally Posted by munclesonkey
T=I/pr
So, when you solved the equation "I = Prt" for "t=", you got t = I/(Pr). That's a start. Now let's return to what I asked you before:

What is the simple-interest formula? What equation then would represent the ending total amount?
To answer the first equation, your answer is "I = Prt". But what is your answer to the second question? What equation represents the ending total amount? That is, not just the interest on the principle, but the entire ending amount?

Then, once you have that equation, solve that equation for "t=". What do you get?