Suppose that $3,000 is placed in an account that pays 8% interest compounded each year assume that no withdrawals are made from the account find the amount in the account at the end of 2 years
The formula for compound interest is
A = P(1 + r/n)^(nt)
where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (the initial amount of money)
r = annual interest rate (in decimal form, so 8% is represented as 0.08)
n = number of times that interest is compounded per year
t = the time the money is invested for in years.
Here, given P = $3000, r = 8% = 0.08, n = 1 (since compounded each year), and t = 2 years, we can substitute these values into the formula:
A = 3000(1 + 0.08/1)^(1*2)
A = 3000(1 + 0.08)^2
A = 3000(1.08)^2
A = 3000*1.1664
A = $3499.20
So, the amount in the account at the end of 2 years would be approximately $3499.20.
To find the amount in the account at the end of 2 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = amount in the account at the end of the time period
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case:
P = $3,000
r = 8% or 0.08 (as a decimal)
n = 1 (compounded annually)
t = 2 years
Using these values, we can calculate the amount in the account:
A = 3000(1 + 0.08/1)^(1*2)
A = 3000(1 + 0.08)^2
A = 3000(1.08)^2
Calculating the exponent:
(1.08)^2 = 1.1664
Now, we can substitute this value back into the equation to find the amount in the account:
A = 3000 * 1.1664
A ≈ $3,499.20
Therefore, the amount in the account at the end of 2 years would be approximately $3,499.20.