Question

Suppose ​$600 is deposited into a savings account that earns ​4% interest compounded annually. Let​ C(t) be the value​ (in dollars) of the account at t years after the ​$600 has been deposited. Find an equation of C.

Answer 1

the equation for the value of the savings account at t years is C(t) = 600(1.04)^t.

Explanation:

A = P(1 + r/n)^(nt)

A = the final amount in the account

P = the initial deposit

r = the annual interest rate (as a decimal)

n = the number of times interest is compounded per year

t = the number of years

In this case, the initial deposit (P) is $600, the annual interest rate (r) is 4% or 0.04, and the interest is compounded annually (n = 1).

Using these values, the equation becomes:

C(t) = 600(1 + 0.04/1)^(1*t)

Simplifying further:

C(t) = 600(1.04)