Find the balance in an account that has $700 invested at 5.5% for 4 years compounded semi-annually.
700(1+.055/2)^(2*4) = 869.67
Oh, the joys of compound interest! Let's calculate the balance in your account, shall we?
To start off, I would need to know the compounding period. Did you say it's semi-annually? Alright, I'll keep that in mind.
Now, let's break it down step by step.
First, we need to determine the interest rate per period. Since we are compounding semi-annually, we'll divide 5.5% by 2, giving us 2.75% per half-year.
Next, we calculate the number of periods. In this case, since it's 4 years and we're compounding semi-annually, we have 8 periods (2 periods per year).
Now comes the fun part! We'll use the formula for compound interest:
Balance = Principal * (1 + Rate) ^ Periods
Plug in the values:
Balance = $700 * (1 + 0.0275) ^ 8
Calculating this out, we find that the balance in your account after 4 years would be approximately $832.12! So, there you have it – a little mathematical magic bringing a smile to your face!
To find the balance in an account that has $700 invested at 5.5% for 4 years compounded semi-annually, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final balance
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case:
P = $700
r = 5.5% = 0.055 (converted to decimal form)
n = 2 (compounded semi-annually, meaning twice a year)
t = 4 years
Plugging in these values into the formula, we have:
A = 700(1 + 0.055/2)^(2 * 4)
Simplifying:
A = 700(1.0275)^(8)
Calculating:
A ≈ $822.67
So, the balance in the account after 4 years will be approximately $822.67.
To find the balance in the account, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final account balance
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 = $700 (initial investment)
r = 5.5% = 0.055 (as a decimal)
n = 2 (compounded semi-annually, meaning twice per year)
t = 4 years
Plugging these values into the formula, we get:
A = 700(1 + 0.055/2)^(2*4)
Now, let's solve the equation step by step:
1. Calculate the value inside the parentheses:
(1 + 0.055/2) = 1.0275
2. Raise that value to the power of (2*4):
1.0275^(2*4) = 1.0275^8 = 1.13139375
3. Multiply the result by the principal amount:
700 * 1.13139375 = $791.97
Therefore, the balance in the account after 4 years, compounded semi-annually, would be approximately $791.97.