how much should be deposited in an account paying 10% compounded quarterly in order to have an amount of bire 10,000 after ten years
We can use the formula for compound interest:
A = P (1 + r/n)^(nt)
Where:
A = amount accumulated after t years
P = principal amount (initial amount deposited)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, we want to solve for P, the initial deposit:
P = A / (1 + r/n)^(nt)
We know that A = 10,000, r = 0.1 (10%), n = 4 (quarterly compounding), and t = 10 years:
P = 10,000 / (1 + 0.1/4)^(4*10)
P = 2,595.82
Therefore, an initial deposit of $2,595.82 is needed to have an amount of $10,000 after 10 years with an annual interest rate of 10% compounded quarterly.
ahhh, so close
the bot had everything right until the last line, when it couldn't do the
arithmetic
P*(1 + .10/4)^40 = 10000
P = 100000/(1.025)^40 = $ 3,724.31 , not 2595.82