Write a function that represents the situation. Find the balance A in the account after the given time period t
.
$2000 deposit that earns 5% annual interest compounded quarterly; 5 years
To find the balance A in the account after the given time period t, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A is the final balance
P is the principal amount (initial deposit)
r is the annual interest rate (in decimal form)
n is the number of times the interest is compounded per year
t is the time period in years
In this case, the principal amount is $2000, the annual interest rate is 5% (or 0.05 as a decimal), and the interest is compounded quarterly (n = 4) over a period of 5 years (t = 5).
Substituting these values into the formula, we get:
A = 2000 * (1 + 0.05/4)^(4 * 5)
Now, let's write a function in a programming language like Python that calculates the balance after the given time period:
```python
def calculate_balance(principal, interest_rate, compounding_frequency, time_period):
balance = principal * (1 + interest_rate/compounding_frequency) ** (compounding_frequency * time_period)
return balance
# Example usage
principal = 2000
interest_rate = 0.05
compounding_frequency = 4
time_period = 5
balance = calculate_balance(principal, interest_rate, compounding_frequency, time_period)
print("The balance after {} years is: ${:.2f}".format(time_period, balance))
```
By calling the `calculate_balance` function with the given values, we can find the balance in the account after 5 years.
To represent the situation, we can write a function that calculates the balance A in the account after a given time period t.
The formula for compound interest is given by:
A = P * (1 + r/n)^(n*t)
Where:
A = the balance after t years
P = the principal amount (initial deposit)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
Based on the given information, we have:
P = $2000
r = 5% (or 0.05 in decimal form)
n = 4 (compounded quarterly)
t = 5 years
Let's write the function to calculate the balance:
def calculate_balance(P, r, n, t):
A = P * (1 + r/n) ** (n*t)
return A
Now, let's use this function to find the balance after 5 years:
balance = calculate_balance(2000, 0.05, 4, 5)
print("Balance after 5 years:", balance)
The output will give you the balance after 5 years.
for any interest rate r compounded n times per year, and time t years,
A = P(1 + r/n)^(nt)
so, plug in your numbers.