Answer to Question #122637 in Financial Math for nehal

Question

Suppose that after making 50 payments, the interest rate changes to J2=9% p.a.

Convert the interest rate J2=9% to J12 equivalent
Assuming that the family seeks to accept the change in interest rates, what would be their new payment based on the new interest rate?
Assuming that the family seeks to continue their initial monthly payment, calculated in part I, how many full payments would be required to pay off the loan and what would be the final concluding smaller payment one period later?

Answer 1

Conversion of the interest rate J2=9% to J12 equivalent

J_m = i*m

Nominal interest rate = 9% per annum.

J₂=9% (compounding done twice a year)

J₁₂ = J₂ *2 =9%*2 = 18% /12 =1.5%

Assuming that the family seeks to accept the change in interest rates, what would be their new payment based on the new interest rate?

n= payment after 50^th payment = 360 – 50 = 310

Interest rate per month = 1.5% per month

PMT = $251,000 \times 1.5 \times 1.015 / (1- 1.015^{-310})$

PMT = $ 3,859.68

Full payments would be required to pay off the loan and what would be the final concluding smaller payment one period later

The loan has a repayment period of 30 years.

1 year = 12 months.

30 years = 12* 30 = 360 months.  

Number of payments required to pay off the loan = 360 payments

Final concluding smaller payment one period later

Principal = P₃₆₀-P₃₅₉

Mortgage value to pay over the 360 months period = House value – Deposit amount

Mortgage value = $326,000 - $75,000 = $251,000

P₃₆₀ = 251,000

Monthly payments (PMT) = Principal * Interest rate per month

PMT = 251,000 (0.75%) * (1.0075)³⁶⁰ / ((1.0075)³⁶⁰ -1)

PMT = $ 2019.6

P₃₅₉ = PMT * Interest rate per month

P₃₅₉ = $2019.6 \times (1- (1.0075)^{-359}) / 0.0075$

P₃₅₉ = $  250,862.55  

PMT_final = $ 251,000 - $ 250,862.55  

Final concluding payment = $ 137.45