Question

You have just sold your house for$1,000,000 in cash. Your mortgage was originally a​ 30-year mortgage with monthly payments and an initial balance of$800,000.The mortgage is currently exactly​ 18½ years​ old, and you have just made a payment. If the interest rate on the mortgage is 5.25%

​(APR), how much cash will you have from the sale once you pay off the​ mortgage? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

Cash that remains after payoff of mortgage is ​$

##I need to know how to solve this with BA2 Plus calculator##

Answer 1

Step 1 - Calculation of monthly payment on mortgage
We can use the present value of annuity formula to calculate the monthly payment on mortgage
Present Value of annuity = P x {[1 - (1+r)^-n]/r}
Present value of annuity = initial balance of mortgage = $800000
P = monthly payment on mortgage = ?
r = interest rate per month = 5.25%/12 = 0.004375
n = number of monthly payments = 30 years x 12 = 360
800000 = P x {[1 - (1+0.004375)^-360]/0.004375}
800000 = P x 181.0926
P = 4417.63
Monthly Payment on Mortgage = $4417.63
Step 2 - Calculation of mortgage balance at the time of sale of house i.e.after 18.5 years of mortgage payment
We can use the present value of annuity formula to calculate the current mortgage balance
Present Value of annuity = P x {[1 - (1+r)^-n]/r}
Present value of annuity = current mortgage balance = ?
P = monthly payment on mortgage = 4417.63
r = interest rate per month = 5.25%/12 = 0.004375
n = number of monthly payments remaining = 21.5 years x 12 = 138
Present Value of annuity = 4417.63 x {[1 - (1+0.004375)^-138]/0.004375}
Present Value of annuity = 4417.63 x 103.4336
Present Value of annuity = 456931.41
Current Mortgage Balance = $4,56,931.41
Step 3 - Calculation of Cash that remains after payoff of mortgage
Cash that remains after payoff of mortgage = Sale value of house - Current Mortgage balance
Cash that remains after payoff of mortgage = $10,00,000 - $4,56,931.41
Cash that remains after payoff of mortgage = $5,43,068.59