Convert 1.5% per month into a decimal rate, then find the monthly multiplier (growth factor) you apply to the balance each month.

If the balance changes every month but $t$ is measured in years, how many months (compounding periods) happen in $t$ years? That number should appear as the exponent.

In Desmos, type the expression A = 500*(1.015)^12. This represents what the balance should be after 1 year, because the account is multiplied by 1.015 once for each of the 12 months.

Now enter each choice with $t=1$:

• A1 = 500*(1+0.015*1)
• A2 = 500*(1.015)^1
• A3 = 500*(1.015)^(12*1)
• A4 = 500*(1.18)^1 Desmos will display a numerical value for each expression.

Compare the values of A1, A2, A3, and A4 with the value of A. The function whose value at $t=1$ exactly matches A is the model that correctly represents 1.5% interest compounded monthly.

The problem describes interest that is compounded monthly at a constant rate.

That means:

• Each month, the balance is multiplied by the same growth factor.
• This is exponential growth, which uses a formula of the form

where $P$ is the initial amount, $r$ is the rate per compounding period, and $n$ is the number of compounding periods.

The monthly interest rate is 1.5%.

1. Convert 1.5% to a decimal rate per month:
   $1.5\% = 0.015$.
2. The monthly growth factor is $1 + 0.015 = 1.015$.
   This is what you multiply the balance by each month.
3. If $t$ is in years, then the number of months (compounding periods) is

because there are 12 months in each year.

Now plug everything into the compound interest form $A = P(1+r)^n$:

• Initial amount $P = 500$
• Growth factor per month $1 + r = 1.015$
• Number of months $n = 12t$

So the balance after $t$ years is

This matches answer choice C.