Question
In: Finance
You have decided to buy a house for $600,000. You have saved enough money to make...
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?
Solutions
Expert Solution
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 |
| 23 | $ 4,63,144.60 |
$
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