b$)$ How might they be mathematically related when applied to interest$-$type investments where your money is invested at the beginning of the year? FV $=$ PV x $(1+$ i$)$ n where; Future Value $($FV$)=$ Present Value $($PV$)+$ the accumulated and compounded Interest, $$i$$ is the interest rate and n is the number of years of investment.

$($c$)$ How might they be mathematically related when applied to mining$-$type investments where your investment consists of amounts spent throughout the year and you only receive money back from the mine$$s eventual product sales? Provide some explanation for the difference