Question

Ted places $1500 in a ten-year certificate of deposit (CD) account at a local bank. The CD account earns interest, compounded annually, at the same rate for 10 years.

Let A(n) represent the amount, in dollars, in Ted's account after n years between n = 0 to n = 10.
Part A:
Write an explicit expression for the function A(n) if Ted's account has $1535.25 after 1 year

Answer 1

A(n) = 1500 * (1 + 0.0367)^n

Explanation:

Given that Ted's account has $1535.25 after 1 year, we can use that value to write an explicit expression for the function A(n).

The amount in the account after n years is given by the formula:

A(n) = A(0) * (1 + r)^n

where A(0) is the initial amount in the account and r is the interest rate.

Since A(1) = $1535.25 and A(0) = $1500, we can substitute these values into the formula:

1535.25 = 1500 * (1 + r)^1

Solving for r:

r = (1535.25/1500) - 1 = 0.0367

So, the interest rate is 3.67% and the explicit expression for the function A(n) is:

A(n) = 1500 * (1 + 0.0367)^n