Consider a future value of $$500,7$ years in the future. Assume that the nominal interest rate is $30\mathrm{.}00\%.$

$1.$ If you are calculating the present value of this cash flow under semiannual $($twice per year$)$ compounding, you would enter $($A$.3\mathrm{.}5$ B$.14$ C$.7)$ for N and $($A$\mathrm{.}15$ B$\mathrm{.}62$ C$\mathrm{.}30$ D$\mathrm{.}60)$ for I$/$Y into your financial calculator.

Entering in the values you just calculated for N and I$/$Y$,$ along with a PMT$=0$ and a FV$=$$$500,$ into a financial calculator yields a present value of approximately $ $($A$.12\mathrm{.}6988$ B$.70\mathrm{.}6643$ C$.187\mathrm{.}9685$ D$.79\mathrm{.}6831)$ with semiannual compounding.

$2.$ If you are calculating the present value of this cash flow under quarterly $($four times per year$)$ compounding, you would enter $($A$.7$ B$.28$ C$.11$ D$.1\mathrm{.}75)$ for N and $($A$.120$ B$.30$ C$.7\mathrm{.}5$ D$.124)$ for I$/$Y into your financial calculator.

Entering in the values you just calculated for N and I$/$Y$,$ along with a PMT$=0$ and a FV$=$$$500,$ into a financial calculator yields a present value of approximately $ $($A$\mathrm{.}0\mathrm{.}3225$ B$\mathrm{.}65\mathrm{.}9983$ C$\mathrm{.}301\mathrm{.}3775$ D$\mathrm{.}79\mathrm{.}6832)$ with quarterly compounding.

$3.$ Suppose now that the cash flow of $$500$ only $1$ year in the future.

If you are calculating the present value of this cash flow under quarterly $(12$ times per year$)$ compounding, you would enter $($A$\mathrm{.}12$ B$\mathrm{.}24$ C$\mathrm{.}6$ D$\mathrm{.}1)$ for N and $($A$\mathrm{.}30$ B$\mathrm{.}1\mathrm{.}5$ C$2\mathrm{.}5$ D$\mathrm{.}3\mathrm{.}5)$ for I$/$Y into your financial calculator.

Entering in the values you just calculated for N and I$/$Y$,$ along with a PMT$=0$ and a FV$=$$$500,$ into a financial calculator yields a present value of approximately $ $($A$\mathrm{.}79\mathrm{.}6832$ B$\mathrm{.}371\mathrm{.}7779$ C$\mathrm{.}21\mathrm{.}461$ D$\mathrm{.}420\mathrm{.}6326)$ with monthly compounding.