If C dollars are deposited in an account paying r percent annual interest, approximate the amount in the account after X years if c=$250, r=2.4% and x=23 years?
To calculate the amount in the account after X years, we need to use the formula for compound interest. The formula is:
A = P *(1 + r/n)^(n*t)
Where:
A = the final amount in the account
P = the principal amount (the initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years
In this case, the principal amount is $250, the annual interest rate is 2.4% (or 0.024 in decimal form), and the number of years is 23.
Since the question does not specify the number of times interest is compounded per year, we will assume it is compounded annually (n = 1).
Now, let's substitute the given values into the formula:
A = $250 * (1 + 0.024/1)^(1*23)
Now, calculate the exponent:
A = $250 * (1.024)^23
Using a calculator, calculate the exponent first, then multiply by $250:
A ≈ $250 * 1.71713151123
A ≈ $429.28 (rounded to two decimal places)
Therefore, the approximate amount in the account after 23 years would be approximately $429.28.