Question

Suppose you take out a $107,000, 20-year mortgage loan to buy a condo. The interest rate on the loan is 4%. To keep things simple, we will assume you make payments on the loan annually at the end of each year.

a. What is your annual payment on the loan? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. Construct a mortgage amortization. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

c. What fraction of your initial loan payment is interest? (Do not round intermediate calculations. Enter your answers as a whole percent.)

d. What fraction of your initial loan payment is amortization? (Do not round intermediate calculations. Enter your answers as a whole percent.)

e. What fraction of the loan has been paid off after 10 years (halfway through the life of the loan)? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

f. If the inflation rate is 1%, what is the real value of the first (year-end) payment? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

g. If the inflation rate is 1%, what is the real value of the last (year-end) payment? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

h. Now assume the inflation rate is 7% and the real interest rate on the loan is unchanged. What must be the new nominal interest rate? (Do not round intermediate calculations. Enter your answers as a whole percent.)

i-1. Recompute the amortization table. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

i-2. What is the real value of the first (year-end) payment in this high-inflation scenario? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

j. What is the real value of the last payment in this high-inflation scenario? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

a)

Annual payment of loan= Loan Amount/PVAF(4%,20 years) =107000/13.5903

= $7,873.25

b) Mortgage amortization Schedule

Years	Opening Balance	Installment	Interest @4%	Principal repayment	Closing Balance
1	$        107,000.00	$   7,873.25	$       4,280.00	$                      3,593.25	$      103,406.75
2	$        103,406.75	$   7,873.25	$       4,136.27	$                      3,736.98	$         99,669.78
3	$            99,669.78	$   7,873.25	$       3,986.79	$                      3,886.46	$         95,783.32
4	$            95,783.32	$   7,873.25	$       3,831.33	$                      4,041.91	$         91,741.40
5	$            91,741.40	$   7,873.25	$       3,669.66	$                      4,203.59	$         87,537.81
6	$            87,537.81	$   7,873.25	$       3,501.51	$                      4,371.73	$         83,166.08
7	$            83,166.08	$   7,873.25	$       3,326.64	$                      4,546.60	$         78,619.47
8	$            78,619.47	$   7,873.25	$       3,144.78	$                      4,728.47	$         73,891.01
9	$            73,891.01	$   7,873.25	$       2,955.64	$                      4,917.61	$         68,973.40
10	$            68,973.40	$   7,873.25	$       2,758.94	$                      5,114.31	$         63,859.09
11	$            63,859.09	$   7,873.25	$       2,554.36	$                      5,318.88	$         58,540.20
12	$            58,540.20	$   7,873.25	$       2,341.61	$                      5,531.64	$         53,008.57
13	$            53,008.57	$   7,873.25	$       2,120.34	$                      5,752.90	$         47,255.66
14	$            47,255.66	$   7,873.25	$       1,890.23	$                      5,983.02	$         41,272.64
15	$            41,272.64	$   7,873.25	$       1,650.91	$                      6,222.34	$         35,050.30
16	$            35,050.30	$   7,873.25	$       1,402.01	$                      6,471.24	$         28,579.06
17	$            28,579.06	$   7,873.25	$       1,143.16	$                      6,730.08	$         21,848.98
18	$            21,848.98	$   7,873.25	$           873.96	$                      6,999.29	$         14,849.69
19	$            14,849.69	$   7,873.25	$           593.99	$                      7,279.26	$            7,570.43
20	$              7,570.43	$   7,873.25	$           302.82	$                      7,570.43	$                  -0.00

c) Fration of Initial loan payment is Interest= $7873.25-($107000*.04)= $4280 which is 54.36%{(4280/7873.25)-1}

d) Fraction of intital loan payment was amortization = 100%-53.36%= 45.64% or ($7873.25-$4280)/$7873.25= 45.64%