Problem $1$: The Basic Solow Model $[18$ Points$]$

Consider an economy with a savings rate of

Problem $2$: Present Value $[6$ Points$]$

Consider a bond that you could buy. This bond pays out $$4,000$ four years from now. This bond also pays a coupon payment of $$200$ two years from now and a second $$200$ payment three years from now. The interest rate of $10\%.$

$10.$ What is the Present Value of the payments from this bond? $[2$ points$]$

Now suppose that at the beginning of two years from now $($before the first coupon payment is given out$),$ this individual has an option to not receive their second coupon payment, and instead increase their first coupon payment to $$350.$

$11.$ Should this individual take this option? $[2$ points$]$

Finally, suppose that this individual can buy this bond, including its coupon payments and the option, for a price of $$3,200.$

$12.$ What would be the present value of the benefits of this bond minus the present value of the costs of this bond, assuming that this bond includes the option from Q$11?$ Should this individual buy this bond? $[$Hint: This is called the Net$-$Present Value $($NPV$)][2$ points$]$

Problem $2$: Present Value $[6$ Points$]$

Consider a bond that you could buy. This bond pays out $$4,000$ four years from now. This bond also pays a coupon payment of $$200$ two years from now and a second $$200$ payment three years from now. The interest rate of $10\%.$

$10.$ What is the Present Value of the payments from this bond? $[2$ points$]$

Now suppose that at the beginning of two years from now $($before the first coupon payment is given out$),$ this individual has an option to not receive their second coupon payment, and instead increase their first coupon payment to $$350.$

$11.$ Should this individual take this option? $[2$ points$]$

Finally, suppose that this individual can buy this bond, including its coupon payments and the option, for a price of $$3,200.$

$12.$ What would be the present value of the benefits of this bond minus the present value of the costs of this bond, assuming that this bond includes the option from Q$11?$ Should this individual buy this bond? $[$Hint: This is called the Net$-$Present Value $($NPV$)][2$ points$]$

Problem $2$: Present Value $[6$ Points$]$

Consider a bond that you could buy. This bond pays out $$4,000$ four years from now. This bond also pays a coupon payment of $$200$ two years from now and a second $$200$ payment three years from now. The interest rate of $10\%.$

$10.$ What is the Present Value of the payments from this bond? $[2$ points$]$

Now suppose that at the beginning of two years from now $($before the first coupon payment is given out$),$ this individual has an option to not receive their second coupon payment, and instead increase their first coupon payment to $$350.$

$11.$ Should this individual take this option? $[2$ points$]$

Finally, suppose that this individual can buy this bond, including its coupon payments and the option, for a price of $$3,200.$

$12.$ What would be the present value of the benefits of this bond minus the present value of the costs of this bond, assuming that this bond includes the option from Q$11?$ Should this individual buy this bond? $[$Hint: This is called the Net$-$Present Value $($NPV$)][2$ points$]$