A company deposits $5,000 in a bank account that earns 3% compound interest each year.which function represents the value,V(t),in dollars,of the bank account after t years?
$5000 (1 + .03)^t
To represent the value, V(t), in dollars of the bank account after t years, you can use the compound interest formula:
V(t) = P(1 + r/n)^(nt)
Where:
- V(t) is the value of the bank account after t years
- P is the principal amount (initial deposit), which is $5,000 in this case
- r is the annual interest rate expressed as a decimal, which is 3% or 0.03 in this case
- n is the number of times interest is compounded per year, which is typically not specified in the question. Assuming it's compounded annually, n would be 1.
Plugging in these values, the function becomes:
V(t) = 5000(1 + 0.03/1)^(1*t)
Simplifying further:
V(t) = 5000(1 + 0.03)^t
Therefore, the function that represents the value of the bank account after t years is V(t) = 5000(1.03)^t.
To represent the value of the bank account after t years with compound interest, we need to use the formula for compound interest:
V(t) = P(1 + r/n)^(nt)
Where:
V(t) is the value of the bank account after t years.
P is the principal amount, which is $5,000 in this case.
r is the annual interest rate, which is 3% expressed as a decimal, so r = 0.03.
n is the number of times interest is compounded per year. Since it's not specified, we'll assume it's compounded annually, so n = 1.
t is the number of years, which varies depending on the question.
Putting the values into the formula, we have:
V(t) = 5000(1 + 0.03/1)^(1t)
Simplifying further:
V(t) = 5000(1.03)^t
Therefore, the function that represents the value, V(t), in dollars, of the bank account after t years is V(t) = 5000(1.03)^t.