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NAME: Today, Mr. Smith wishes to purchase a house which costs $400,000.00. His bank requires a 25% down payment and will lend
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Answer #1

a) To calculate the monthly payment

  • Cost of house = 400,000
  • Down payment = 25%
    • Down payment = 25% x 400,000
    • Down payment = 100,000
  • Loan amount = Cost of house - down payment
    • Loan amount = 400,000 - 100,000
    • Loan amount = 300,000
  • We are given the following information
  • Payment PMT Need to calculate
    Interest rate r 6.00%
    Years n 30
    Monthly frequency 12
    Loan amount PV $   300,000.00
  • We need to solve the following equation to arrive at the required PMT
  • 1- 1+ Frequency _)-nx frequency PV = PMT X- frequency -30x12 300000 = PMT X- 1- (1 + 0.06 0.06 12 PMT = 1798.65

b) Mortgage schedule is as follows:

Month Opening Balance PMT Principal repayment Closing Balance | 3,00,000.00 $ 298.65 | 2,99,701.35 1| 3,00,000.00 $ 1,798.65

  • Opening balance = previous year's closing balance
  • Closing balance = Opening balance+Loan-Principal repayment
  • PMT is calculated as per the above formula
  • Interest = 0.06 /12 x opening balance
  • Principal repayment = PMT - Interest

C)Total interest paid is  $347,514.57

D) In first year the total interest paid is the sum of the first 12 interest payments which equals 17,899.78

E) If the monthly payment is 1600 then the balloon payment is calculated as follows:

We need to follow the below steps:

  1. First we will have to find the FV of the loan amount at the end of 30 years
  2. Find the FV of the 1600 monthly payment at the end of year 30
  3. Subtract the FV of monthly payment from the FV of the loan amount
  4. The resultant amount is balloon payment

Step 1) We are given the following information:

PV $        3,00,000.00
r 6.00%
n 30
frequency 12
Future value of FV need to calculate

We need to solve the following equation to arrive at the required FV:

FV = PV X (1+1 frequency frequencyxn 0.06 12x30 FV = 300000 X (1+. FV = 1, 806, 772.56

So the FV of the loan is 1,806,772.56

Step 2) We are given the following information:

PMT $              1,600.00
r 6.00%
n 30
Frequency 12

We need to solve the following equation to arrive at the required FV

(1+ r )nx Frequency - 1 FV = PMT X- Frequency (1 + 0.06 ) 30x12 - 1 FV = 1600 x FV = 1,607, 224.07

So the FV of the monthly payments is 1,607,224.07

Step 3) Calculate the balloon payment:

1,806,772.56 - 1,607,224.07 = 199,548.49

Step 4) Bolloon payment = 199,548.49

Below is the schedule with balloon payment:

11111111111111111111111111111111111111111111111111111TTTTTTTTTTTTTTTTTTTTTTTTTTIIIIIIIIIIIIIIIIIIIIIIIIIIIT. 8 Month Opening

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