Align nominal rates, period rates and compounding counts

Consider the education savings fund under a compound-interest model

\(V_k\) is the fund balance, in dollars, after \(k\) compounding periods. \(V_0\) is the value now. Let \(p\) be the number of compounding periods per year and let \(y\) be the number of years

Interest is compounded monthly, so \(p\)=12

The nominal annual rate is 8.1%. Interest is added to the current fund balance at the end of each compounding period. The initial balance is $42,000 and the model covers 4 years