Question 1 (20 marks)

Mr. Chan saves $1,000 per year at the beginning of each year for 8 years, starting from today. The original payments earn 5% annual interest, but the interest received on the payments will be taken out and put into another account earning 3% annual interest. How much will Mr. Chan have at the end of 8 years?

Question 2 (15 marks)

John wanted to purchase a house at price $7million. He planned to borrow 80% of the total amount through mortgage loan provided by HSBC. HSBC charged him an annual interest rate at Prime Rate minus 4% and he had to pay off the loan in 25 years. The first payment was made one month after the purchase when the prime rate was 8%. 10 years later, HSBC adjusted the prime rate to 10%.

What is the monthly payment during 10^th year to 25^th year?

Question 3: (Total 15 marks)

You would like to purchase a new home for $4.5million. You have obtained a 30-year mortgage loan from a bank with annual interest rate 4%. However, you can afford monthly payment of only $12,000, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single bullet payment.

How large will this bullet payment have to be for you to keep your monthly payments at $12,000?

Question 4 (10 marks)

You are currently aged 30. There is an investment planning suggests that if you invest $5,000 per month, you can receive a monthly payment in return after you retired at aged 65 until you died with 2 percent annual growth rate. Suppose the annual interest rate is 3 percent, how much is the first payment to be received at the 1^st month after retirement?