a = 24000 [1 + (.04 / 12)]^(30 * 12)
4% interest, compounded monthly
4% interest, compounded monthly
A = P(1 + r/n)^(nt)
Where:
A = the final amount (including both the principal and interest)
P = the principal amount (the initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $24,000, the annual interest rate (r) is 4% (or 0.04 as a decimal), the number of times interest is compounded per year (n) is 12 (monthly compounding), and the number of years (t) is 30.
Plugging these values into the formula, we can calculate the final amount (A):
A = 24000(1 + 0.04/12)^(12*30)
Simplifying the calculation step by step:
A = 24000(1 + 0.003333)^(360)
A = 24000(1.003333)^(360)
A ≈ 24000(1.370370)
A ≈ 32968.88
Therefore, the final amount, including both the principal and compound interest, would be approximately $32,968.88 after 30 years.