Question

Suppose you deposit $500 into an account earning 7.8% interest compounded annually (grows every year). Which equation models the balance of the account after x number of years?

A. y = 500(7.8)^x
B. y = 500(1.78)^x
C. y = 500(1.078)^x
D. y = 500(0.922)^x

Answer 1

The correct equation modeling the balance of an account after x years with $500 deposited at 7.8% interest compounded annually is C. y = 500(1.078)^x. This models the balance growing by an annual factor of 1.078.

Step-by-step explanation:

The equation that models the balance of an account after x number of years when you deposit a principal amount at a certain interest rate compounded annually is given by:

y = Principal(1 + interest rate)x

In this case, the equation would be the initial deposit $500 growing at 7.8% compounded annually. Therefore, the correct equation is:

C. y = 500(1.078)x

This equation reflects that each year, the new balance is 1.078 times the balance of the previous year, representing the principal plus 7.8% interest.