You deposit $$2000$ into a saving plan at the end of each year for three years. The historical rate of return is equivalent to $10\%$ per year compounded annually.

a$.$ Assuming the historical rate of return, find the value of the annuity after three years.

b$.$ Find the earnings from this investment.

At the age of $30,$ to save for retirement, you decide to deposit $$100$ at the end of each month into an IRA that earns the equivalent of $9\mathrm{.}5\%$ compounded monthly.

a$.$ How much will you have from the IRA when you retire at age $65?$

b$.$ Find the earnings from this investment.

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