$1$ Ann got a $10$ year Fixed Rate Mortgage for $$100,000.$

The loan has constant annual payments and an annual interest rate of $5\%.$

There are no closing costs.

Suppose Ann prepays the loan in year $4.$

Write the NPV of Ann's Mortgage $($from Ann's perspective$)$ for an annual discount rate $"k"$ in each of the following

cases.

Note: the answer must take the form $NPV(k)=C{F}_0+\frac{C{F}_1}{(1+k{)}^1}+\frac{C{F}_2}{(1+k{)}^2}+\frac{C{F}_8}{(1+k{)}^3}+\frac{C{F}_4}{(1+k{)}^4}$

Note: only include one cash$-$flow for each time period

$1$a Fully Amortizing

$1$b Partially Amortizing where the final balance is $B_{10}=$$$50,000$

$1$c Interest Only

$1d$ Negatively Amortizing where the payment is $PMT=$$$1,000$

$1$e Negatively Amortizing where the payment is $PMT=$$$0$

$2$ Compute the IRR for each loan above

$2a$

$2b$

$2$c

$2d$

$2e$

Can you solve $2$a to $2$e please.