Question

A $198,000 mortgage amortized by monthly payments over 20 years is renewable after five years. Interest is 4.65% compounded semi-annually. Complete parts (a) though (e) below. (a) What is the size of the monthly payments? The size of a monthly payment is $ (Round to the nearest cent as needed.) (b) How much interest is paid during the first year? The interest paid in the first year is $ (Round to the nearest cent as needed.) (c) ow much of the principal is repaid during first five-year term? The amount of the principal repaid during the first five-year term is $ (Round to the nearest cent as needed.) (d) If the mortgage is renewed for a further five-year term at 5.24% compounded semi-annually, what will be the size of the monthly payments? The size of the monthly payments is $ (Round to the nearest cent as needed.) (e) Construct a partial amortization schedule showing details of the first three payments for each of the two five-year terms. Complete the schedule for the first three payments of the first five-vear term.

Answer 1

Mortgage size = $198,000

Tenure = 20 years with monthly repayments

Interest = 4.65% compounded semi-annually

Since the mortgage is renewable after each 5 years, the rate of 4.65% is applicable for this 5-year term.

Since the 4.65% rate is compounded semi-annually and the payments are to be made monthly, we need to arrive at the effective annual rate first and then divide the same by 12 to arrive at the monthly interest rate.

Effective annual rate = ( 1 + (0.0465/2))^2 - 1 = 4.704%

Thus, Monthly interest rate = 4.704%/12 = 0.392%

We need to use this monthly interest rate to arrive at the monthly payment for this 20 year mortgage using the PMT function in Excel or a Financial calculator. Using the same we get the following:

Answer a. Size of the monthly payment is $1,274.56

The first 5-year amortization table is given below using the above payment :

Mortgage principal outstanding	Monthly payment	Interest payment	Principal payment
$198,000.00	$1,274.56	$776.17	$498.39
$197,501.61	$1,274.56	$774.22	$500.34
$197,001.26	$1,274.56	$772.25	$502.31
$196,498.96	$1,274.56	$770.29	$504.27
$195,994.68	$1,274.56	$768.31	$506.25
$195,488.43	$1,274.56	$766.32	$508.24
$194,980.20	$1,274.56	$764.33	$510.23
$194,469.97	$1,274.56	$762.33	$512.23
$193,957.74	$1,274.56	$760.32	$514.24
$193,443.50	$1,274.56	$758.31	$516.25
$192,927.25	$1,274.56	$756.28	$518.28
$192,408.97	$1,274.56	$754.25	$520.31
$191,888.67	$1,274.56	$752.21	$522.35
$191,366.32	$1,274.56	$750.16	$524.39
$190,841.92	$1,274.56	$748.11	$526.45
$190,315.47	$1,274.56	$746.05	$528.51
$189,786.96	$1,274.56	$743.97	$530.59
$189,256.37	$1,274.56	$741.89	$532.67
$188,723.71	$1,274.56	$739.81	$534.75
$188,188.95	$1,274.56	$737.71	$536.85
$187,652.10	$1,274.56	$735.61	$538.95
$187,113.15	$1,274.56	$733.49	$541.07
$186,572.08	$1,274.56	$731.37	$543.19
$186,028.89	$1,274.56	$729.24	$545.32
$185,483.57	$1,274.56	$727.10	$547.46
$184,936.12	$1,274.56	$724.96	$549.60
$184,386.52	$1,274.56	$722.80	$551.76
$183,834.76	$1,274.56	$720.64	$553.92
$183,280.84	$1,274.56	$718.47	$556.09
$182,724.75	$1,274.56	$716.29	$558.27
$182,166.48	$1,274.56	$714.10	$560.46
$181,606.02	$1,274.56	$711.90	$562.66
$181,043.37	$1,274.56	$709.70	$564.86
$180,478.50	$1,274.56	$707.48	$567.08
$179,911.43	$1,274.56	$705.26	$569.30
$179,342.13	$1,274.56	$703.03	$571.53
$178,770.60	$1,274.56	$700.79	$573.77
$178,196.83	$1,274.56	$698.54	$576.02
$177,620.81	$1,274.56	$696.28	$578.28
$177,042.53	$1,274.56	$694.02	$580.54
$176,461.99	$1,274.56	$691.74	$582.82
$175,879.17	$1,274.56	$689.45	$585.11
$175,294.06	$1,274.56	$687.16	$587.40
$174,706.66	$1,274.56	$684.86	$589.70
$174,116.96	$1,274.56	$682.55	$592.01
$173,524.95	$1,274.56	$680.23	$594.33
$172,930.61	$1,274.56	$677.90	$596.66
$172,333.95	$1,274.56	$675.56	$599.00
$171,734.95	$1,274.56	$673.21	$601.35
$171,133.59	$1,274.56	$670.85	$603.71
$170,529.89	$1,274.56	$668.49	$606.07
$169,923.81	$1,274.56	$666.11	$608.45
$169,315.36	$1,274.56	$663.72	$610.84
$168,704.53	$1,274.56	$661.33	$613.23
$168,091.30	$1,274.56	$658.93	$615.63
$167,475.66	$1,274.56	$656.51	$618.05
$166,857.61	$1,274.56	$654.09	$620.47
$166,237.14	$1,274.56	$651.66	$622.90
$165,614.24	$1,274.56	$649.22	$625.34
$164,988.90	$1,274.56	$646.76	$627.80

Answer b. Using the above table, total interest paid during the 1st year is $9,183.39

Answer c. Using the above table, total principal paid during the 5-year period is $33,638.90

Now, once the mortgage is renewed for a further 5-year term at a rate of 5.24% compounded semi-annually, we will have to repeat the above procedure to calculate the monthly payment and construct anamortization table with principal outstanding being $198,000.00 - $33,638.90 = $164,361.10 and balance tenure of 15 years.

Answer d. Using these data points, the size of the monthly payment is $1,326.34

The next 5-year amortization table is given below using the above payment:

Answer e. The partial amortization table showing details of the 1st three payments for each of the two 5-year terms is given below:

For 1st 5-year period:

Mortgage principal outstanding	Monthly payment	Interest component	Principal component
$198,000.00	$1,274.56	$776.17	$498.39
$197,501.61	$1,274.56	$774.22	$500.34
$197,001.26	$1,274.56	$772.25	$502.31

For the 2nd 5-year period:

Mortgage principal outstanding	Monthly payment	Interest payment	Principal payment
$164,361.10	$1,326.34	$727.11	$599.22
$163,761.88	$1,326.34	$724.46	$601.87
$163,160.00	$1,326.34	$721.80	$604.54