Question

To offset the cost of buying a $100,000 house, Julia borrowed $22,500 from her parents at 6% nominal interest, compounded monthly. The loan from her parents is to be paid off in five years in equal monthly payments. She has saved $21,250. Her total down payment is therefore $22,500 + 21,250 = $43,750. The balance will be mortgaged at 9% nominal interest, compounded monthly for 30 years. Find the combined monthly payment that Julia will be making for the first five years.To offset the cost of buying a $100,000 house, Julia borrowed $22,500 from her parents at 6% nominal interest, compounded monthly. The loan from her parents is to be paid off in five years in equal monthly payments. She has saved $21,250. Her total down payment is therefore $22,500 + 21,250 = $43,750. The balance will be mortgaged at 9% nominal interest, compounded monthly for 30 years. Find the combined monthly payment that Julia will be making for the first five years.

Answer 1

Answer- The combined monthly payment that Julia will be making for the first five years
=EMI paid to his parents and EMI paid for mortgage
= 434.99+452.60= 887.59 or $ 888/month.
Explanation
Given
Total cost of house= $ 100000
She has save $ 21250
She borrowed from her parents $ 22500
Total down payment was made
= 21250+22500= $ 43750
Remaining balance
= total cost - down payment
=100000-43750= $ 56250
Thus, she will take mortgage of $ 56250.

Interest rate on borrowing from her parents is 6% p.a. or 6/12=0.5% per month.
EMI= {P*R*(1+R)^n}/[{(1+R)^n}-1]
Where P is Principal=22500
R is interest rate/month= 0.5% or 0.005
N is number of payment= 12*5=60
EMI= {22500*0.005*(1+0.005)^60}/[{(1+0.005)^60}-1]
EMI={112.5*(1.005)^60}/[{(1.005)^60}-1]
EMI=(112.5*1.34885)/(1.34885-1)
EMI= 151.7456/0.34885
EMI= 434.99 or $ 435.
She will pay to her parents $ 434.99 or $ 453/month.

Interest rate on mortgage is 9% p.a.or 9/12= 0.75%/month
EMI= {P*R*(1+R)^n}/[{(1+R)^n}-1]
Where P is Principal=56250
R is interest rate= 0.75% or 0.0075
N is number of payment= 12*30=360
EMI= {56250*0.0075*(1+0.0075)^360}/[{(1+0.0075)^360}-1]
EMI={421.875*(1.0075)^360}/[{(1.0075)^360}-1]
EMI=(421.875*14.73)/(14.73-1)
EMI= 6214.22/13.73
EMI=452.60 or $ 453.
She will pay for mortgage $ 452.60 or $ 453/month.