Consider a dollar amount of $$1,000$ today, along with a nominal interest rate of $18\mathrm{.}00\%.$ You are interested in calculating the future value of this amount after $7$ years.

For all future value calculations, enter $$$$1,000($with the negative sign$)$ for PV and $0$ for PMT$.$

When calculating the future value of $$1,000,$ compounded annually for $7$ years, you would enter a value of for N$,$ a value of for I$/$Y$.$

Using the keystrokes you just identified on your financial calculator, the future value of $$1,000,$ compounded annually for $7$ at the given nominal interest rate, yields a future value of approximately $.$

When calculating the future value of $$1,000,$ compounded semi$-$annually $($twice per year$)$ for $7$ years, you would enter a value of for N$,$ a value of for I$/$Y$.$

Using the keystrokes you just identified on your financial calculator, the future value of $$1,000,$ compounded semi$-$annually for $7$ at the given nominal interest rate, yields a future value of $.$

When calculating the future value of $$1,000,$ compounded quarterly for $7$ years, you would enter a value of for N$,$ a value of for I$/$Y$.$

Using the keystrokes you just identified on your financial calculator, the future value of $$1,000,$ compounded quarterly for $7$ at the given nominal interest rate, yields a future value of $.$

When calculating the future value of $$1,000,$ compounded monthly for $7$ years, you would enter a value of for N$,$ a value of for I$/$Y$.$

Using the keystrokes you just identified on your financial calculator, the future value of $$1,000,$ compounded monthly for $7$ at the given nominal interest rate, yields a future value of $.$

Hint: Assume that there are $365$ days in a year.

When calculating the future value of $$1,000,$ compounded daily for $7$ years, you would enter a value of for N$,$ a value of for I$/$Y$.$

Using the keystrokes you just identified on your financial calculator, the future value of $$1,000,$ compounded daily for $7$ at the given nominal interest rate, yields a future value of $.$

Based on the results of your calculations, you can conclude that $($all else equal$)$ more frequent compounding leads to a future value. This is due to a periodic interest for more frequent compounding.

Step $3$: Practice: Future Value for Various Compounding Periods

Now it$$s time for you to practice what you$$ve learned.

Consider a dollar amount of $$1,000$ today, along with a nominal interest rate of $15\mathrm{.}00\%.$ You are interested in calculating the future value of this amount after $4$ years.

For all future value calculations, enter $$$$1,000($with the negative sign$)$ for PV and $0$ for PMT$.$

The future value of $$1,000,$ compounded annually for $4$ at the given nominal interest rate, is approximately $.$

Using your financial calculator, the future value of $$1,000,$ compounded semi$-$annually for $4$ at the given nominal interest rate, is approximately $.$

Using your financial calculator, the future value of $$1,000,$ compounded quarterly for $4$ at the given nominal interest rate, is approximately $.$

Using your financial calculator, the future value of $$1,000,$ compounded monthly for $4$ at the given nominal interest rate, is approximately $.$

Hint: Assume that there are $365$ days in a year.

Using your financial calculator, the future value of $$1,000,$ compounded daily for $4$ at the given nominal interest rate, is approximately $.$