Question

Juliet has a 10-year mortgage of $500,000 with an interest rate of 3.5% APR, compounded quarterly. Mortgage payments are made at the beginning of each month. What is the balance remaining on this mortgage after the 60th payment? PLEASE DO NOT GIVE THE INCORRECT ANSWER of

Find first month rate as given rate is compounded quarterly (1 + r)^12 = (1 + 0.035/4)^4 r = (1 + 0.035/4)^(1/3) – 1 = 0.002908 = 0.2908% Set up the TVM parameters PV = $500,000, r = 0.002908, N = 120, FV = 0; compute PMT =? PV = 500,000 = (PMT/0.002908)*(1 – 1/1.002908^120) PMT = 4941.91 Monthly payment = $4941.91 Again setup the TVM parameters PV = $500,000, r = 0.002908, N = 60, PMT = 4941.91; compute FV =? PV = 500,000 = (4941.91/0.002908)*(1 – 1/1.002908^60) + FV/1.002908^60 FV = 271,724.92 Amount left after 60th payment = $271,724.92 Thank you.

Answer 1

Effective annual rate = (1+r/n)^n - 1
= (1 + 3.5% / 4)^4 - 1
= 3.5462%

Monthly rate = (1 + 3.5462%)^(1/12) - 1 = 0.2908%

PV = 500000

Nper = 10 * 12 = 120

FV = 0

Monthly pauments can be calculated by using the following excel formula:
=PMT(rate,nper,pv,fv,beginning of the period)
=PMT(0.2908%,120,-500000,0,1)
= $4927.58

Monthly payments = $4927.58

Balance remaining on this mortgage after the 60th payment can be calculated by using the following excel formula:
=PV(rate,nper,pmt.fv)
=PV(0.2908%,120-60,-4927.58,0)
= $270,936.98 or $270,937

Balance remaining on this mortgage after the 60th payment = $270,936.98 or $270,937