Question

Amortization schedules a. Set up an amortization schedule for a $250,000 mortgage to be repaid in equal monthly installments at the end of each month for the next 15 years. The mortgage rate is an APR of 4.5%. b. How large must each monthly payment be if the loan is for $500,000? Assume that the interest rate remains at 4.5% and that the loan is paid off over 15 years. c. How large must each monthly payment be if the loan is for $500,000, the interest rate is 4.5%, and the loan is paid off in equal installments at the end of each month for the next 30 years? This loan is for the same amount as the loan in part b, but the payments are spread out over twice as many periods. Why are these payments not half of the payments on the loan in part (b)?

Please show work in excel

Answer 1

a)

EMI = P*i*(1+i)^n/[{(1+i)^n}-1]

Where,

P = Principal = 250000

i= Interest Rate = 0.045/12 = 0.00375

n= Number of periods = 15*12 = 180

Therefore, EMI = 250000*0.00375*(1+0.00375)^180/[{(1+0.00375)^180}-1]

= 937.5*(1.961555)/[1.961555-1] = $1912.4

b)

EMI = P*i*(1+i)^n/[{(1+i)^n}-1]

Where,

P = Principal = 500000

i= Interest Rate = 0.045/12 = 0.00375

n= Number of periods = 15*12 = 180

Therefore, EMI = 500000*0.00375*(1+0.00375)^180/[{(1+0.00375)^180}-1]

= 1875*(1.961555)/[1.961555-1] = $3824.97

c)

EMI = P*i*(1+i)^n/[{(1+i)^n}-1]

Where,

P = Principal = 500000

i= Interest Rate = 0.045/12 = 0.00375

n= Number of periods = 30*12 = 360

Therefore, EMI = 500000*0.00375*(1+0.00375)^360/[{(1+0.00375)^360}-1]

= 1875*(3.847698)/[3.847698-1] = $2533.43

The Payments are not HALF of payments in b) because, Interest Payable will INCREASE due to HIGHER TENURE.