I.Find the present and future value of $1000 received every month end for 20 years if the interest rate is J12 = 12% p.a. (5 marks)

II.Find the present value of $10,000 received at the start of every year for 20 years if the interest rate is J1 = 12% p.a. and if the first payment of $10,000 is received at the end of 10 years. (5 marks).

III.John is currently 25 years old. He has $10,000 saved up and wishes to deposit this into a savings account which pays him J12 = 6% p.a. He also wishes to deposit $X every month into that account so that when he retires at 55, he can withdraw $2000 every month end to support his retirement. He expects to live up till 70 years. How much should he deposit every month into his account? (10 Marks)

QUESTION 2: LOAN AMORTIZATION [35 MARKS]

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? (1 mark)

B.Find the value of the monthly payment? (3 marks)

C.Find the loan outstanding after making 20 payments? (4 marks)

D.Find the principal repaid in the 21^st payment? (5 marks)

II. Fill out the loan amortization schedule provided in the solution template for the first 5 loan payments. What do you notice about the composition of the payment amount? (6 marks)

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)