Find total amount in compound interest account.
$9000 IS compounded semiannually at a rate of 11% for 20 years
round to the nearest hundredths as needed
With compound interest, the interest due and paid at the end of the interest compounding period is added to the initial starting principal to form a new principal, and this new principal becomes the amount on which the interest for the next interest period is based. The original principal is said to be compounded, and the difference between the the final total, the compound amount, accumulated at the end of the specified interest periods, and the original amount, is called the compound interest.
In its most basic use, if P is an amount deposited into an account paying a periodic interest, then Sn is the final compounded amount accumulated where
...........Sn = P(1+i)^n
where i is the periodic interest rate in decimal form = %Int./(100m), n is the number of interest bearing periods, and m is the number of interest paying periods per year.
Sn = P(1+i)^n
Sn = 9000(1.055)^40 = $76,619.78
To calculate the total amount in a compound interest account, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A is the total amount
P is the principal amount
r is the interest rate (as a decimal)
n is the number of times interest is compounded per year
t is the number of years
In this case, the principal amount (P) is $9000, the interest rate (r) is 11% (or 0.11 as a decimal), the interest is compounded semiannually (n = 2), and the number of years (t) is 20.
Let's substitute these values into the formula:
A = 9000(1 + 0.11/2)^(2*20)
A = 9000(1 + 0.055)^(40)
A = 9000(1.055)^40
Calculating this using a calculator, we get:
A ≈ $48,019.53
Therefore, the total amount in the compound interest account after 20 years would be approximately $48,019.53.
To find the total amount in a compound interest account, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment or starting amount)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, we have:
P = $9000
r = 11% (or 0.11 as a decimal)
n = 2 (since it is compounded semiannually, twice in a year)
t = 20 years
Substituting these values into the formula:
A = 9000(1 + 0.11/2)^(2*20)
Now, let's calculate this equation.