You deposit $500 into an account that pays 3% annual interest, compounded monthly. Write an exponential model that describes the situation and allows you to find the balance after t years.

Answer 1

Let “M” be money in the account

Let “t” be number of years→

3/12 = 0.25(%) → monthly interest

M = 500(1.0025)^12t → money in the account after “t” years

Answer 2

The formula we want to use here is for annual interest, compounded n times per year.

t: time (in yrs) , the independent variable

A(t): account value (in $) , the dependent variable

A(t) = A₀ · (1 + r/n)^nt , where A₀ is the initial investment (principal), r is the annual interest rate (expressed as a decimal), and n is the number of times / year the interest is compounded.

For your specific question, we would have A(t) = 500 · (1 + .03/12)^12t or A(t) = 500 · (1.0025)^12t

Answer 3

A(t) = 500(1 + 0.03/12)¹²t, where t is time in years.