You deposit $4000 each year into an account earning 6% interest compounded annually. How much will you have in the account in 30 years?
amount = 4000( 1.06^30 - 1)/.06
= ....
To calculate the total amount in the account after 30 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/total amount in the account
P = the principal amount (initial deposit)
r = annual interest rate (expressed as a decimal)
n = number of times the interest is compounded per year
t = time in years
In this case, the principal amount (P) would be the sum of the annual deposits, which is $4000. The annual interest rate (r) is 6% or 0.06 in decimal form. The interest is compounded annually, so n = 1. And t = 30 years.
Plugging in these values into the formula, we get:
A = 4000(1 + 0.06/1)^(1*30)
Simplifying further:
A = 4000(1 + 0.06)^30
Using a calculator, we can evaluate the expression:
A ≈ 4000 * (1.06)^30 ≈ $15,717.82
After 30 years of depositing $4,000 annually into an account with an annual interest rate of 6% compounded annually, you will have approximately $15,717.82 in the account.
To calculate the future value of the account after 30 years, you can use the formula for compound interest:
Future Value = Principal x (1 + Rate)^Time
Where:
Principal = $4000 (the amount you deposit each year),
Rate = 6% (0.06 as a decimal, the interest rate),
Time = 30 years.
Now let's substitute these values into the formula:
Future Value = $4000 x (1 + 0.06)^30
First, let's simplify the calculation inside the parentheses by adding 1 to the interest rate:
Future Value = $4000 x (1.06)^30
Next, let's calculate (1.06)^30:
(1.06)^30 ≈ 2.2079
Now, multiply $4000 by 2.2079 to get the final answer:
Future Value ≈ $4000 x 2.2079 ≈ $8831.60
Therefore, after 30 years, you will have approximately $8831.60 in the account.