Question

You have decided to buy a house for $600,000. You have saved enough money to make a 20% down payment, but you will need to borrow the remainder. You arrange for a 30-year mortgage (monthly payments) with a local bank at a stated rate of 3.6% APR. a) What will be your monthly payment? b) Construct the amortization table for the first 12 months of payments (showing how much of your payment goes to principal, how much goes to interest, and the remaining balance on the loan). c) What will be the outstanding balance or remaining principal after 24 monthly payments? In other words, if you decided to pay off the loan after 24 months, how much would you owe?

Answer 1

Loan Required = Price ( 1 -Down Payment Ratio )

= $ 600000 ( 1 - 0.2 )

= $ 600000 * 0.8

= $ 480000

Part A:

Particulars	Amount
Loan Amount	$         4,80,000.00
Int Rate per month	0.3000%
No. of Months	360

EMI = Loan Amount / PVAF (r%, n)
Where r is Int rate per month & n is no. of months
= $ 480000 / PVAF (0.003 , 360)
= $ 480000 / 219.9517
= $ 2182.3

PVAF = SUm [ PVF(r%, n) ]
PVF(r%, n) = 1 / ( 1 + r)^n
r = Int rate per period
n = No. of periods

Part B:

Period	Opening Bal	EMI	Int	Principal Repay	Closing Outstanding
1	$         4,80,000.00	$         2,182.30	$            1,440.00	$                742.30	$            4,79,257.70
2	$         4,79,257.70	$         2,182.30	$            1,437.77	$                744.52	$            4,78,513.18
3	$         4,78,513.18	$         2,182.30	$            1,435.54	$                746.76	$            4,77,766.42
4	$         4,77,766.42	$         2,182.30	$            1,433.30	$                749.00	$            4,77,017.42
5	$         4,77,017.42	$         2,182.30	$            1,431.05	$                751.25	$            4,76,266.18
6	$         4,76,266.18	$         2,182.30	$            1,428.80	$                753.50	$            4,75,512.68
7	$         4,75,512.68	$         2,182.30	$            1,426.54	$                755.76	$            4,74,756.92
8	$         4,74,756.92	$         2,182.30	$            1,424.27	$                758.03	$            4,73,998.89
9	$         4,73,998.89	$         2,182.30	$            1,422.00	$                760.30	$            4,73,238.59
10	$         4,73,238.59	$         2,182.30	$            1,419.72	$                762.58	$            4,72,476.01
11	$         4,72,476.01	$         2,182.30	$            1,417.43	$                764.87	$            4,71,711.14
12	$         4,71,711.14	$         2,182.30	$            1,415.13	$                767.16	$            4,70,943.97

Opening Bal = Previous Month closing baance

Instalment = EMI as calculated in Part A

Int = Opening Balance * 0.3%

Principal repay = Instalment - Int

CLsoing Balance = Opening Balnce - Principal Repay

Int - 17131.55

Principal - 9056.03

CLosing Balance - 470943.97

Part C:

Period	Opening Bal	EMI	Int	Principal Repay	Closing Outstanding
1	$         4,80,000.00	$         2,182.30	$            1,440.00	$                742.30	$            4,79,257.70
2	$         4,79,257.70	$         2,182.30	$            1,437.77	$                744.52	$            4,78,513.18
3	$         4,78,513.18	$         2,182.30	$            1,435.54	$                746.76	$            4,77,766.42
4	$         4,77,766.42	$         2,182.30	$            1,433.30	$                749.00	$            4,77,017.42
5	$         4,77,017.42	$         2,182.30	$            1,431.05	$                751.25	$            4,76,266.18
6	$         4,76,266.18	$         2,182.30	$            1,428.80	$                753.50	$            4,75,512.68
7	$         4,75,512.68	$         2,182.30	$            1,426.54	$                755.76	$            4,74,756.92
8	$         4,74,756.92	$         2,182.30	$            1,424.27	$                758.03	$            4,73,998.89
9	$         4,73,998.89	$         2,182.30	$            1,422.00	$                760.30	$            4,73,238.59
10	$         4,73,238.59	$         2,182.30	$            1,419.72	$                762.58	$            4,72,476.01
11	$         4,72,476.01	$         2,182.30	$            1,417.43	$                764.87	$            4,71,711.14
12	$         4,71,711.14	$         2,182.30	$            1,415.13	$                767.16	$            4,70,943.97
13	$         4,70,943.97	$         2,182.30	$            1,412.83	$                769.47	$            4,70,174.51
14	$         4,70,174.51	$         2,182.30	$            1,410.52	$                771.77	$            4,69,402.73
15	$         4,69,402.73	$         2,182.30	$            1,408.21	$                774.09	$            4,68,628.64
16	$         4,68,628.64	$         2,182.30	$            1,405.89	$                776.41	$            4,67,852.23
17	$         4,67,852.23	$         2,182.30	$            1,403.56	$                778.74	$            4,67,073.49
18	$         4,67,073.49	$         2,182.30	$            1,401.22	$                781.08	$            4,66,292.41
19	$         4,66,292.41	$         2,182.30	$            1,398.88	$                783.42	$            4,65,508.99
20	$         4,65,508.99	$         2,182.30	$            1,396.53	$                785.77	$            4,64,723.22
21	$         4,64,723.22	$         2,182.30	$            1,394.17	$                788.13	$            4,63,935.09
22	$         4,63,935.09	$         2,182.30	$            1,391.81	$                790.49	$            4,63,144.60
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