$5650 is compound semiannually at a rate of 16% for 14 years how much is the total amount in the compound interest account?
what is
5650(1.08)^28 ?
Wow, you are getting 16% interest?
Must be a very old textbook
To find the total amount in the compound interest account, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Total amount in the account (including principal and interest)
P = Principal amount (initial deposit)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case:
P = $5650
r = 16% = 0.16 (convert the percentage to decimal form)
n = 2 (semiannually means compounded twice a year)
t = 14 years
Plugging in these values into the formula, we get:
A = 5650(1 + 0.16/2)^(2*14)
To simplify the calculation, let's break it down step-by-step.
Step 1: Calculate the interest rate per compounding period:
The interest rate per compounding period is 16% divided by 2 (since the interest is compounded twice a year):
16% / 2 = 0.08
Step 2: Calculate the total number of compounding periods:
The total number of compounding periods is given by multiplying the number of years by the number of times compounded per year:
2 * 14 = 28
Step 3: Calculate the total amount in the account:
A = 5650(1 + 0.08)^(28)
Now you can use a calculator or a spreadsheet program to evaluate this expression.
A ≈ $19,636.04
So, the total amount in the compound interest account after 14 years will be approximately $19,636.04.