Question

1. Suppose you take a fixed-rate mortgage for $200,000 at 5.00% for 30 years, monthly payments.

   A. (1 pt) How much of the payment is interest for month 100?
   Answer: ________

B. (1 pt) How much interest do you pay in the first six years?
Answer: ________

Answer 1

(a)

Monthly Payment = rP(1+r)^N/[(1+r)^N-1]

For monthly compounding,

r = 0.05/12

N = 30*12 = 360 months

P = 200000

=> Monthly Payment = 200000*( 0.05/12)*(1+ 0.05/12)³⁶⁰/((1+ 0.05/12)³⁶⁰-1) = $1073.64

(b)

Amount paid in 6 years = 1073.64*6*12 = $77302.08

Balance Principal after p month is given by

B = P[(1 + r)ⁿ - (1 + r)^p]/[(1 + r)ⁿ - 1]

Balance Principal after 6 years (p = 12*6 = 72 months)

B = 200000[(1 + 0.05/12)³⁶⁰ - (1 + 0.05/12)⁷²]/[(1 + 0.05/12)³⁶⁰ - 1] =$179870.61

Principal Amount Paid in 6 years = 200000 - 179870.61 = $20129.39

Hence, Interest Paid = Amount Paid in 6 years - Principal remaining after 6 years = 77302.08 - 20129.39 = $57172.69