Suppose that P dollars are invested in a savings account at interest rate I, compounded annually, for 2 years. The amount A in the account after 2 years is given by A = P(1 + i)^2. Find an equivalent polynomial expression for A.
Please help if you can!
Thank you! :-)
expand (1+i)^2
(I don't know why anybody would want to do that in this case)
Do you mean (1 + i)(1+ i)?
Find the amount of money in an account after 10 years if a principal of $2500 is invested at 3.5% invested compounded quartely.
To find an equivalent polynomial expression for A, we can expand the expression (1 + i)^2 and simplify it.
Starting with the expression:
A = P(1 + i)^2
We can use the distributive property to expand the square:
A = P(1 + i)(1 + i)
Using the FOIL method (First, Outer, Inner, Last), we can multiply the binomials:
A = P(1 * 1 + 1 * i + i * 1 + i * i)
Simplifying, we have:
A = P(1 + i + i + i^2)
Since i^2 means i * i, we can simplify further:
A = P(1 + 2i + i^2)
Now, since P is just a constant, we can distribute it across the terms:
A = P + 2Pi + Pi^2
Finally, rearranging the terms in descending order of i, we get the equivalent polynomial expression for A:
A = Pi^2 + 2Pi + P
So, the polynomial expression for A is Pi^2 + 2Pi + P.