Compound Interest: You deposit $1000 in an account with an annual interest rate of r (in decimal form) compounded monthly. At the end of 5 years, the balance is
A = 1000(1 + (r/12)) ^60
To calculate the balance of the account at the end of 5 years with monthly compounded interest, we can use the formula:
A = P(1 + (r/n))^(nt)
Where:
A is the final account balance
P is the initial deposit amount
r is the annual interest rate in decimal form
n is the number of compounding periods per year
t is the number of years
In this case, we have:
P = $1000 (initial deposit)
r = r (annual interest rate as a decimal)
n = 12 (compounded monthly)
t = 5 (number of years)
So, the formula becomes:
A = 1000(1 + (r/12))^(12*5)
Simplifying:
A = 1000(1 + r/12)^60
Therefore, the balance in the account at the end of 5 years is 1000(1 + r/12)^60.
To calculate the balance at the end of 5 years, you need to 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 = 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, you have:
P = $1000
r = r (the annual interest rate given in decimal form)
n = 12 (compounded monthly, so 12 times per year)
t = 5 (5 years)
Now you can substitute these values into the formula:
A = 1000(1 + (r/12))^(12*5)
Simplifying the equation further:
A = 1000(1 + (r/12))^60
This formula calculates the balance at the end of 5 years, taking into account the initial deposit, the interest rate, and the compounding frequency.