Supposed Susan places $9,000 in an account that pays 12% 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 future value of the investment
P = the principal investment (initial amount)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = time the money is invested for (in years)
In this case, the principal investment (P) is $9,000, the annual interest rate (r) is 12% or 0.12 (in decimal form), interest is compounded yearly so n is 1, and the money is invested for 2 years (t).
Plugging these values into the formula gives:
A = $9,000(1 + 0.12/1)^(1*2)
A = $9,000(1 + 0.12)^2
A = $9,000(1.12)^2
A = $9,000 * 1.2544
A = $11,289.60
So, the amount in the account at the end of 2 years is approximately $11,289.60.
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 = the final amount
P = the principal amount (the initial deposit)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case, Susan places $9,000 in an account with an interest rate of 12% compounded yearly, so:
P = $9,000
r = 0.12 (12% expressed as a decimal)
n = 1 (compounded annually)
t = 2 (2 years)
Let's substitute the values into the formula and calculate the final amount in the account:
A = $9,000(1 + 0.12/1)^(1*2)
A = $9,000(1 + 0.12)^2
A = $9,000(1.12)^2
A = $9,000(1.2544)
A ≈ $11,289.60
Therefore, the amount in the account at the end of 2 years will be approximately $11,289.60.