# Question: i a family buys a house worth 326000 they pay...

###### Question details

I. A family buys a house worth $326,000. They pay $75,000 deposit and take a mortgage for the balance at J12=9% p.a. to be amortized over 30 years with monthly payments.

a. Find the value of the mortgage on their house?

b. Find the value of the monthly payment?

c. Find the loan outstanding after making 20 payments?

d. Find the principal repaid in the 21^{st} payment?

II. Fill out the loan amortization schedule provided below for the first 5 loan payments. What do you notice about the composition of the payment amount? Show working for ending loan balance.

Payment Number |
Beginning Loan Balance |
Payment Amount |
Interest Expense |
Principal Repayment |
Ending Loan Balance |

1 |
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2 |
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3 |
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4 |
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5 |

III. Suppose that after making 50 payments, the interest rate changes to J2=9% p.a.:

a. Convert the interest rate J2=9% to J12 equivalent (2 marks

b. Assuming that the family seeks to accept the change in interest rates, what would be their new payment based on the new interest rate? (5 marks)

c. Assuming that the family seeks to continue their initial monthly payment calculated in part I, how many full payments would be required to pay off the loan and what would be the final concluding smaller payment one period later? (9 marks)