Question

1. 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?

Select one:

a. $216,077

b. $270,937

c. $275,065

d. $266,797

e. $250,000

Answer 1

Answer:

Correct answer is:

b. $270,937

Explanation:

APR = 3.5% compounded quarterly

Effective annual rate = (1 + 3.5%/ 4) ⁴ - 1

= 3.546206%

Monthly interest rate = (1 + 3.546206%) ^(1/12) - 1

= 0.290820%

Duration = 10 years = 120 months

Loan amount = $500,000

Monthly installment paid at the beginning of period = PMT (rate, nper, pv, fv, type)

= PMT (0.290820%, 120, -500000, 0, 1)

= $4927.58

Monthly installment paid at the beginning of period = $4927.58

Balance remaining on this mortgage after the 60th payment = Present value of remaining monthly installments

Remaining monthly installments = 120 - 60 = 60 months

Hence:

Balance remaining on this mortgage after the 60th payment = PV (rate, nper, pmt, fv, type)

= PV (0.290820%, 60, -4927.58, 0,0)

= $270,936.77

= $270,937

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

As such option b is correct and other options a, c, d and e are incorrect.