Question

Dr. Jun bought a $330000 house 7 years ago. The house is now worth $627000. Originally, the house was financed by paying 35% down with the rest financed through a 20-year mortgage at 6% interest. After making 84 monthly house payments, he is now in need of cash, and would like to refinance the house. The finance company is willing to loan 85% of the current value of the house amortized over 25 years at 4% interest.

How much cash will Dr. Jun receive after paying the balance of the original loan?

Amount of cash obtained = $__________

If he uses all of the available cash for something other than investing in his home, by how much will his monthly payment increase?

Increase in monthly payment = $__________

Answer 1

Answer 1
Step 1
Calculation of monthly loan payment on original loan
We can use the present value of annuity formula to calculate the monthly loan payment.
Present value of annuity = P x {[1 - (1+r)^-n]/r}
Present value of annuity = original loan amount = Cost of house - down payment = $330000 - ($330000 x 35%) = $2,14,500
P = monthly loan payment = ?
r = interest rate per month = 6%/12 = 0.005
n = number of monthly loan payments = 20 years x 12 = 240
214500 = P x {[1 - (1+0.005)^-240]/0.005}
214500 = P x 139.5808
P = 1536.74
Monthly loan payment = $1536.74
Step 2
Calculation of orignal loan balance after making 84 monthly house payments
We can use the present value of annuity formula to calculate the loan balance.
Present value of annuity = P x {[1 - (1+r)^-n]/r}
Present value of annuity = original loan balance = ?
P = monthly loan payment = 1536.74
r = interest rate per month = 6%/12 = 0.005
n = number of monthly loan payments remaining = 240 - 84 = 156
Present value of annuity = 1536.74 x {[1 - (1+0.005)^-156]/0.005}
Present value of annuity = 1536.74 x 108.1404
Present value of annuity = 166184.24
Original loan balance after making 84 monthly house payments = $1,66,184.24
Step 3
Calculation of amount of cash will Dr. Jun receive after paying the balance of the original loan
Amount of cash Dr.Jun will receive = New loan amount - Original loan balance as of today
New Loan amount = House's today's worth x 85% = $627000 x 85% = $5,32,950
Amount of cash Dr.Jun will receive = $532950 - $166184.24
Amount of cash will Dr. Jun receive after paying the balance of the original loan = $3,66,765.76
Answer 2
Calculation of monthly loan payment on new loan
We can use the present value of annuity formula to calculate the monthly loan payment.
Present value of annuity = P x {[1 - (1+r)^-n]/r}
Present value of annuity = new loan amount = $532950
P = monthly loan payment = ?
r = interest rate per month = 4%/12 = 0.0033
n = number of monthly loan payments = 25 years x 12 = 300
532950 = P x {[1 - (1+0.0033)^-300]/0.0033}
532950 = P x 189.4525
P = 2813.11
Monthly loan payment on new loan = $2,813.11
Increase in monthly payment = Monthly loan payment on New Loan - Monthly loan payment on original loan
Increase in monthly payment = $2813.11 - $1536.74
Increase in monthly payment = $1276.36