amount = 2000(1 + .05/4)^20
= ...
$2000 deposit that earns 5% annual interest compounded quarterly; 5 years
A function is A=
The balance of the account after 5 years is $_
= ...
A = P(1 + r/n)^(nt)
Where:
A = balance after time period t
P = initial deposit
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = time period in years
In this case:
P = $2000
r = 5% = 0.05 (annual interest rate as a decimal)
n = 4 (quarterly compounding)
t = 5 years
Plugging in these values, the function becomes:
A = 2000(1 + 0.05/4)^(4*5)
Simplifying the expression inside the parentheses (1 + 0.05/4):
A = 2000(1.0125)^(20)
Calculating the result:
A ≈ 2000(1.28218584071)
A ≈ $2564.37
Therefore, the balance of the account after 5 years is approximately $2564.37.
So, the function representing the situation is:
A = 2000(1 + 0.05/4)^(4*5)
A = P(1 + r/n)^(nt)
Where:
A = Balance in the account after the given time period
P = Principal amount (initial deposit)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Time period in years
In this case:
P = $2000 (Initial deposit)
r = 5% = 0.05 (Annual interest rate in decimal form)
n = 4 (Interest is compounded quarterly)
t = 5 (5 years)
Now we can substitute these values into the formula to find the balance A:
A = 2000(1 + 0.05/4)^(4*5)
Simplifying the calculation:
A = 2000(1.0125)^(20)
A ≈ $2553.68
Therefore, the balance A in the account after 5 years is approximately $2553.68.
The function representing this situation is:
A = 2000(1 + 0.05/4)^(4*t)