A bank issues a standard 30-year fixed rate mortgage at 7.8% for $150,000. Thirty-six months later, mortgage rates jump to 13%. If the bank sells the mortgage, how much of a loss is incurred?

when issued require payment is

PV = $150000

I = 7.8/12

N =30 year = 30*12 =360 months

FV = 0

compute PMT = $1079.81

after 36 months mortage balance is

PMT = $1,079.81, I = 7.8/12, N = 324, FV = 0

Compute PV. PV = $145,764.43

However, at current rates, the remaining cash flows are worth:

PMT = $1,079.81, I = 13/12, N = 324, FV = 0

Compute PV. PV = $96,637.64

bank expects to take a loss of $49,126 if it sells the mortgage.

How do you get the $1079.81?

How do you get the $145,764.43

How do you get $96,637.64