$1-$Consider a dollar amount of $$750$ today, along with a nominal interest rate of $15\mathrm{.}00\%.$ You are interested in calculating the future value of this amount after $7$ years.

For all future value calculations, enter $$$$750($with the negative sign$)$ for PV and $0$ for PMT$.$

When calculating the future value of $$750,$ compounded annually for $7$ years, you would enter a value of $\_\_\_\_\_\_\_(0,6,8,7)$ for N$,$ a value of $\_\_\_\_\_\_\_(1\mathrm{.}5,16\mathrm{.}5,7\mathrm{.}5,15)$ for I$/$Y$.$

Using the keystrokes you just identified on your financial calculator, the future value of $$750,$ compounded annually for $7$ at the given nominal interest rate, yields a future value of approximately $\_\_\_\_\_\_\_\_.$

When calculating the future value of $$750,$ 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 $$750,$ compounded semi$-$annually for $7$ at the given nominal interest rate, yields a future value of $\_\_\_\_\_\_\_\_\_\_.$

When calculating the future value of $$750,$ 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 $$750,$ compounded quarterly for $7$ at the given nominal interest rate, yields a future value of $\_\_\_\_\_\_\_\_\_\_\_.$

When calculating the future value of $$750,$ 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 $$750,$ 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 $$750,$ 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 $$750,$ 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.

$2-$Consider a dollar amount of $$750$ today, along with a nominal interest rate of $12\mathrm{.}00\%.$ You are interested in calculating the future value of this amount after $8$ years.

For all future value calculations, enter $$$$750($with the negative sign$)$ for PV and $0$ for PMT$.$

The future value of $$750,$ compounded annually for $8$ at the given nominal interest rate, is approximately $\_\_\_\_\_\_\_\_\_\_\_\_\_.$

Using your financial calculator, the future value of $$750,$ compounded semi$-$annually for $8$ at the given nominal interest rate, is approximately $\_\_\_\_\_\_\_\_\_\_\_\_.$

Using your financial calculator, the future value of $$750,$ compounded quarterly for $8$ at the given nominal interest rate, is approximately $\_\_\_\_\_\_\_\_\_\_\_.$

Using your financial calculator, the future value of $$750,$ compounded monthly for $8$ 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 $$750,$ compounded daily for $8$ at the given nominal interest rate, is approximately $\_\_\_\_\_\_\_\_\_\_\_\_\_.$

$3-$ Consider a deposit into a bank with a stated interest rate $6\%,$ compounded quarterly, for $2$ years.

The periodic interest rate is $\_\_\_\_\_\_\_\_\_(24,4,6,1\mathrm{.}5)\%$ and the number of periods would be $\_\_\_\_\_\_\_\_\_\_\_(2,6,8,4).$

$4-$ Suppose Lorenzo receives a $$28,000\mathrm{.}00$ loan to be repaid in equal installments at the end of each of the next $3$ years. The interest rate is $3\%$ compounded annually.

In this case, PVAN equals $\_\_\_\_\_\_,$ I equals $\_\_\_\_\_\_,$ and N equals $\_\_\_\_\_\_\_.$

Using the formula for the present value of an ordinary annuity, the annual payment amount for this loan is $\_\_\_\_\_\_\_.$

Because this payment is fixed over time, enter this annual payment amount in the $$Payment$$ column of the following table for all three years.

Each payment consists of two parts$$interest and repayment of principal. You can calculate the interest in year $1$ by multiplying the loan balance at the beginning of the year $($PVAN$)$ by the interest rate $($I$).$ The repayment of principal is equal to the payment $($PMT$)$ minus the interest charge for the year:

The interest paid in year $1$ is $\_\_\_\_\_\_\_\_\_\_\_\_.$

Because the balance at the end of the first year is equal to the beginning amount minus the repayment of principal, the ending balance for year $1$ is $\_\_\_\_\_\_\_\_\_.$ This is $\_\_\_\_\_\_\_\_\_\_$ the beginning amount for year $2.$