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Consider a future value of $$500,8$ years in the future. Assume that the nominal interest rate is $9\mathrm{.}00\%.$

If you are calculating the present value of this cash flow under semiannual $($twice per year$)$ compounding, you would enter ${16}_g$rad for $N$ and $4\mathrm{.}5$ for I$/$Y into your financial calculator.

Entering in the values you just calculated for $N$ and $\frac{\text{I}}{Y},$ along with a $PMT=0$ and a $FV=$$$500,$ into a financial calculator yields a present value of approximately $${250\mathrm{.}9331}_g$rad with semiannual compounding.

If you are calculating the present value of this cash flow under quarterly $($four times per year$)$ compounding, you would enter $32$ for I$/$Y into your financial calculator.

Entering in the values you just calculated for $N$ and $\frac{\text{I}}{Y},$ along with a $PMT=0$ and a $FV=$$$500,$ into a financial calculator yields a present value of approximately $ with quarterly compounding.

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 $1_{?}$ for $N$ and $9_{?}$ for $\frac{\text{I}}{Y}$ into your financial calculator.

Entering in the values you just calculated for $N$ and $\frac{\text{I}}{Y},$ along with a PMT $=0$ and a $FV=$$$500,$ into a financial calculator yields a present value of approximately $${470\mathrm{.}9877}_{v}v$ with monthly compounding.

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