What is the net present value of the following reverse mortgage loan to a lender? Assume the first possible termination is one year after origination, and the loan can only terminate on an anniversary of the loan closing. Question $4$

What is the net present value of the following reverse mortgage loan to a lender? Assume the

first possible termination is one year after origination, and the loan can only terminate on an

anniversary of the loan closing.

Initial loan amount $($all drawn at origination$)$: $$200,000$

Initial property value: $$400,000$

loan interest rate: $6\%$

lender discount rate: $4\%$

home price growth rate: $2\%$

hazard rate into termination each year: $3\%,$ unless loan balance exceeds value of home, in

which case $1\%$

Loan terminates no later than $30$ years after origination $($terminates for sure at year $30$ if

hasn't already$)$ Question $5$

What is the net present value of the following reverse mortgage loan to a lender? Assume the

first possible termination is one year after origination, and the loan can only terminate on an

anniversary of the loan closing.

Initial loan amount $($all drawn at origination$)$: $$200,000$

Initial property value: $$400,000$

loan interest rate: $6\%$

lender discount rate: $4\%$

home price growth rate: $2\%$

hazard rate into termination each year: $3\%,$ unless loan balance exceeds value of home, in

which case $1\%$

Loan terminates no later than $40$ years after origination $($terminates for sure at year $30$ if

hasn't already$)$

Initial loan amount $($all drawn at origination$)$: $$200,000$

Initial property value: $$400,000$

loan interest rate: $6\%$

lender discount rate: $4\%$

home price growth rate: $2\%$

hazard rate into termination each year: $3\%,$ unless loan balance exceeds value of home, in which case $1\%$

A$)$ Loan terminates no later than $30$ years after origination $($terminates for sure at year $30$ if hasn't already$)$

B$)$Loan terminates no later than $40$ years after origination $($terminates for sure at year $30$ if hasn't already$)$