Answer to Question #121719 in Financial Math for Talei

Question

III. Suppose that after making 50 payments, the interest rate changes to J2=9% p.a.:
A. Convert the interest rate J2=9% to J12 equivalent
B. Assuming that the family seeks to accept the change in interest rates, what would be
their new payment based on the new interest rate?
C. 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?
So Sir, i would i calculate this

Answer 1

A. Convert the interest rate J₂=9% to J₁₂ equivalent 

Jm = i*m

Nominal interest rate = 9% per annum.

J₂=9%

Periodic rate:

J₁₂ = J₂ *2 =9%*2 = 18% /12 =1.5% 

B. New payment

Tmonths = 30*12 = 360 months

No. of months/payments remaining after 50th payment = 360 – 50 = 310

J₁₂ = 9% compounded semi-annually = 9%*2 = 18%

Interest rate per month = 18% / 12 = 1.5% per month

PMT = 251,000 * (1.5%) * (1.015) / ((1- (1.015)^-310)

PMT = $ 3,802.64  

C. No. of full payments:

I=7.5% =0.0075

No. of payments = 30*12 = 360 payments.

Final concluding smaller payment one period later

Principal = P₃₆₀-P₃₅₉

Full payment: P₃₆₀ = 251,000

P₃₅₉ = 2019.6 * (1- (1.0075)^-359) / (0.0075)

P₃₅₉ = $  250,862.55  

PMT = $ 251,000 - $ 250,862.55 

PMT = $ 137.45