Find the balance in the account after the given period.
Please explain this to me I can't understand the formula.
$3500 deposit earning 6.75% compounded monthly, after 6 months.
To find the balance in the account after the given period, you can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (balance)
P = the principal amount (initial deposit)
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, the principal amount is $3500, the annual interest rate is 6.75% (or 0.0675 as a decimal), and interest is compounded monthly (n = 12 per year). The time is given as 6 months, so t = 6/12 = 0.5 (in years).
Plugging in the given values into the formula:
A = 3500(1 + 0.0675/12)^(12*0.5)
Simplifying inside the parentheses:
A = 3500(1.005625)^(6)
Calculating the exponent:
A = 3500(1.033651)
Finding the final amount:
A ≈ $3601.28
So, the balance in the account after 6 months would be approximately $3601.28.