Suppose you take out a $$105,000,20-$year mortgage loan to buy a condo. The interest rate on the loan is $5\%.$ To keep things simple, we will assume you make payments on the loan annually at the end of each year.

a$.$ What is your annual payment on the loan?

b$.$ Construct a mortgage amortization.

c$.$ What fraction of your initial loan payment is interest?

d$.$ What fraction of your initial loan payment is amortization?

e$.$ What is the total of the loan amount paid off after $10$ years $($halfway through the life of the loan$)?$

f$.$ If the inflation rate is $3\%,$ what is the real value of the first $($year$-$end$)$ payment?

g$.$ If the inflation rate is $3\%,$ what is the real value of the last $($year$-$end$)$ payment?

h$.$ Now assume the inflation rate is $6\%$ and the real interest rate on the loan is unchanged. What must be the new nominal interest rate?

i$-1.$ Recompute the amortization table.

i$-2.$ What is the real value of the first $($year$-$end$)$ payment in this high$-$inflation scenario?

j$.$ What is the real value of the last payment in this high$-$inflation scenario?